SInce the original idea for this thread has run it's course I think it's best to use it for the reason I wanted to homebrew some spells in particular:

The lack of choice of Lightning-Damage Spells in the Tempest Clerics skil-set.

My current choice of homebrew Spells by Spell Level:

Cantrips:
Storm Strike

1st Level:
Invoke Holy Weaponry

2nd Level:
Static Cloud

3rd Level:
Storm Surge

The angle of a cone is set in the PHB and cannot be changed, a 5-foot cone would only ever hit 1 creature. 

your spell is absolutely nothing like G-FB, and much more like some of the Ranger spells.

What are you actually trying to represent with this? It sounds to me like some kind of a sweeping weapon attack, in which case I don't think you really need the cone. I'd just describe it something like:

Lightning Strike

You can hit up to three adjacent enemies that you can reach with one of your held melee weapons. Roll an attack for that weapon against each enemy, dealing lightning damage equal to your spellcasting modifier + 2d8 instead of the normal damage.

The damage dice improve to 3d8 at 3rd level, 2d12 at 5th level and 3d12 at 7th level.

Something like that? Then all you need to do is copy Green-Flame Blade's template, don't bother adding a cone anywhere, you just want the damage to appear as a reminder next to weapons like it does for Green-Flame Blade.

I will say however that damage and scaling is really weird; the starting damage is extremely high (this would be hands down the single most powerful damaging cantrip in the game beyond what any other cantrip can do). I'm curious why it scales this way?

I just changed the ability, since I realized it didnt need to be a weapon attack. It uses nothing from my Weapon. 
It's atm just a melee "Cast" that uses my weapon within it.

The original reason for me homebrewing this at all is the severe lack of Lightning Spells/Abilities on Tempest Clerics.
Literally only 1 Spell and 1 Class Feature can use their Channel Divinity Feature at all, unless you either go for an initiate feat (which then uses a different spellcasting mod).

So I tried to come up with 1 cantrip and 1 level 1 spell that were based on some more variety to use Channel Divinity on, especially as Martial Options for Melee Clerics similar to Hexblade Warlocks.

The Spell is a slightly buffed version of Hex.

A concentration Spell that lasts up 1 hour and lets me add 1d6 / 1d8 / 1d10 / 1d12 of Lightning Damage to Damage rolls on Attacks at 1st, 3rd, 5th and 6th level respectively. As a Downside it can't be transferred from 1 enemy to another and doesnt impart disadvantage to their ability checks. 

When trying to come up with a Cantrip I wanted to replicate the Melee Caster Vibe that Hexblade has with GFB.

At first I was just trying to make a Cantrip that allows me to modify any action to replace a damage dice with Lightning Damage and rerolling 1s in the respective damage roll.
But I was struggling to represent this through Homebrew. 

So I came up with something similar to the Primal Strike Skill in Grim Dawn (if you know what that is)
Which is basically just the ability to fluff a spell into an AoE melee attack (especially since I couldnt find any "Wide Swing" homebrew rules for trying to hit multiple people with one attack)

When going for Damage I tried to scale it in a way that would help me balance the damage for use against single targets and groups alike, so it wouldnt be a catch-all. That's why the dice were scaling weirdly.

I still dont think my scaling works out well. I think I need a way to diversify it's usability by defining it's damage differently for use against multiple/single enemies.

I just didnt want to jump the shark and just take existing homebrew and be creative myself.

I had some different ideas though:

A concentration Spell that lets me choose between:
Turning my Weapon Damage to Lightning and adding an additional Spellcast Mod in Damage to it
or casting a lightning nova for xd4 damage around me with x being 1d6
As an Action on my next turn if my COncentration isn't broken

but that left me at wanting to make a lot of concentration spells which I am already frustrated by on Warlocks (like 90% of Warlock Spells are concentration)

So here I am trying to balance a Melee AoE Cantrip.

Best place to start with homebrew if you need it to be balanced is to copy something as similar to what you want as possible; for example, we might not have a lightning AoE cantrip, but we do have a thunder AoE cantrip in Thunderclap, so a lightning cantrip should probably be about the same as that. If you modify it to only target those in front (max 3 vs. max 8), then you could justify increasing the dice from d6's to d8's, or maybe d10's, but to be balanced the scaling would need to remain the same.

I feel your pain on the lack of "storm" spells though; I'm playing a Tempest Cleric based character mixed with Storm Sorcerer, and actually both of those sub-classes are a bit limited in their choices at certain levels. We've got Shocking Grasp as a melee cantrip option at least, and it's a good one to have (being able to attack and essentially disengage is always nice), but nothing ranged except the weirdly terrible Lightning Lure (Thorn Whip is much better).

For that character I created two different options; Arc and Lightning Strike (and just realised I reused the name) scaled around what I thought a ranged Shocking Grasp might look like. I'm using the Lightning Strike version on my character, but I created both to consider the possibilities. Although that character doesn't use it, I also made a Chromatic Blade spell as a Shadow Blade equivalent for elemental characters, you might do the same if you want a blade spell but make one that's lightning specific (e.g- advantage vs. metal armour?).

I am still thinking how I want to handle this. 

Eventually my goal is to have a Spell per Spell Level that is unique to Tempest Cleric as well as a cantrip.

With at most one of these being a concentration spell.

I just dont want to copy existing Spells outright. And I mostly want these spells to service Tempest Domains Channel Divinity, by allowing more skills to profit from it for different situations. 

Quote from RhodosGuard >>

I just dont want to copy existing Spells outright. And I mostly want these spells to service Tempest Domains Channel Divinity, by allowing more skills to profit from it for different situations. 

Oh sure, you definitely want to at least tweak them into something that's a bit more interesting; but the best way to get the potency of a spell roughly right is to start from an existing one that's good for its elemental type.

For example for Chromatic Blade, sure it's a Psychic Blade clone, but it has a different trigger for its advantage (target being resistant to that damage type, so it's still useful even when a target resists the damage as you'll be hitting it more).

Plus for damaging spells at least there's going to be at least something that's a bit similar so it's good to start with some frame of reference for amount of damage; in general you shouldn't do more damage than a similar existing spell unless you have a less powerful rider (added benefit) or some kind of drawback (shorter range, smaller radius, more commonly strong save type like Constitution etc.).

Currently sitting at 2 designs I feel comfortable with right now:

Lightning Blade: (Cantrip, A)
Reduces the damage dice from GFB to d6 instead of d8 with the secondary damage instead bursting out against all surrounding enemies.
At max potency my Spell deals less secondary damage, and only 0.5 more damage on average to the main target. 

Only usable with a Weapon wielded with both hands (Versatile or Two-Handed)

At Level 17:
4d6  - main

3d6 + Spell mod - Secondary

Infused with Lightning - 10 Minute Concentration (BA):
Replace up to a certain amount of dice in Damage rolls with Lightning Damage. 
Drop concentration early as a BA to add an additional damage dice of Lightning Damage to the Action you take that turn -> only available for the first few turns, equal to replacable dice, after first cast

The amount of replaceable dice is:
One at 1st level, then an additional dice for every 2 spell levels above 1st.

Hm. For some reason the Spell I created is just "always prepared" for my Tempest cleric, and the Cantrip is Known to me by default and trying to remove it crashes DnD Beyonds API :/

This can happen in some weird circumstances; did you repurpose anything you already created when editing the spell and cantrip?

Sometimes you need to wait for the system to update everything, which can take up to twenty minutes, and it's best not to have the character window open in any browser (as that can stop it refreshing). Sometimes if you can't remove a spell from the character sheet, if you go into the character builder and remove the spell under spells in the class tab then that might work, so you can re-add them to the sheet once they've loaded in properly.

I figured it out. Apparently when adding spells to "Cleric - Tempest Domain" it adds the spells to the domain spell list, and not the general spell list for tempest clerics, so it treats them like Domain Spells, similar to Fog Cloud and Thunderwave, so you will always have them prepared. 

SO you have to put new Tempest Cleric Spells into the generic Cleric List.

I am currently trying to design a spell that allows me to channel my deities power into a weapon temporarily (probably concentration)
But if I put that spell on a low Spell level it will scale out of control even just reaching 5th level.
Like even adding 5d4 to all weapon rolls could be dangerous. 
I tried thinking of unique stuff to add to the skill to compensate for just adding a d4 to damage, but whenever I do it feels either boring or too complex.

I dunno. I am mentally exhausted.

I am happy with my Lightning Blade Cantrip but when it comes to spells most everything just feels generic.

This is my current version for a 10 Minute concentration Spell of 1st level:

Invoke Holy Weaponry:

You plead with your deity to supply you with their signature weapon, or bless your own.

Channeling a Prayer through your Holy Symbol you can choose one of 2 effect:

1. Blessed Weapon - A Blessed Weapon radiates your gods power. It deals 1d6 additional damage, the type of which depends on the deity you worship.
2. Signature Weapon - You materialize one of your gods signature weapons. These weapons are defined by your DM and have a fixed base Weapon. They also bear the bonus damage from Blessed Weapon 

While this spell is active the weapon is considered magical.

While this spell is active, when casting a different spell or cantrip, roll a spellcasting check (1d20)
Based on your roll the following effects will trigger:

DC 11 - you may add 1d4 Damage to the spell, the damage type of which is defined by your deity
DC 15 - your spell deals it's entire damage as your deities main damage, additionally to the DC 11 effect

Both the Bonus Damage on your weapon, as well as the bonus Damage on spells is increased by 1d6 / 1d4 for every second Spell Slot above 1st

It's an interesting idea but it feels overly complex IMO, as you're having to roll a check for every cantrip, when really you could just have the same effect apply to all attacks (which would apply to cantrips a well). You've also got a possible conflict/doubling if a cantrip includes a weapon attack.

Since you're looking at making it a 1st-level spell your points of reference are Divine Favor (add radiant damage to all weapon attacks, no fixed target) or Hex and Hunter's Mark (extra damage and a rider effect but only vs. a single target at a time).

On that basis I'd look at something more like:

Voltaic Prayer (bonus action, 10 minute concentration, vocal & somatic)

You empower your attacks with the fury of the storm. Until the spell ends your attacks deal an additional d4 lightning damage on a hit, and you may choose to swap the attack's normal damage type for lightning as well.

This should be mostly balanced compared to Divine Favor, as while it lasts longer and applies to all attacks (so includes spells) it is using a more resisted damage type.

It should also save you work, as you wouldn't need to add lightning attack spells for other levels, as a player could just pick spells with the effects they want then use this to swap the damage for lightning, which they can maximise using their Channel Divinity.

While I understand the criticism, I actually thought about this in the meantime too, I realized that it really isn't a problem.
Let's look at it like this:
Without my Homebrew Clerics wouldnt even have a Cantrip that includes a Weapon Attack. 

I created it, because I felt like the lore of War/Tempest Clerics was based on a kind of hybridization between Divine Power and Martial Prowess, that I didnt feel like was represented within those classes selection of spells. 

Tempest clerics significantly lacked Lightning Damage despite multiple features literally relying on it. While Cleric in general just missed a lot of Melee Stuff. There is Spirit Guardians, but that is Radiant Damage. 

I mean, when a game gives a class Heavy Armor and Martial Weapon Proficiency at level 1, then they shouldnt drag down the Melee Playstyle by:
Blocking Somatic Components from being used when using a 2-Handed Weapon, and gate that ability behind warcaster
Barely including Melee/Touch/Attack Spells
Making those spells that are available to not be of the Classes main Type.

Now, looking at what you designed, I feel like it hits what i want from a design point. Basically just allow me to chose some spell I want to use and utilize my class feature with it.

The reason I put it behind a Spellcasting Check, is that without that restriction you go out of control at a certain level. I think this is also the reason they dont give him a lot of lightning spells on Vanilla Spell lists.

Imagine being able to Cast Spirit Guardians, and be guaranteed that everytime it dealt damage, you can push an enemy back 10 ft. While ALSO slowing their movement to half.

For a basic creature, that means:
They start their turn within Spirit Guardians Range.
Whether they fail or not, they get pushed back 10 ft. since they suffer lightning damage.
If they fail their safe, they move at half speed. A default creatue can move 20 ft toward you on a success. And 5 ft toward you at a fail. 

In a best case scenario, you could activate the spell, and then stand still while occassionally casting a spell to deal more damage while they struggle to get even near you. 

I know that a spellcasting check for a utility this powerful is also kinda whack. Maybe it oughta be a "on hit" check rather than "on cast" so I dont have a guarantee on every hit. 

Anyway. I would definitely make it a choice: Increased Damage or changing it to lightning. Imagine things like Necromancer spells if you could add Lightning Damage and on top convert the damage to lightning with Channel Divinity.

You'd stand there at level 2 or 3 being able to inflict multiple d12 as guaranteed Lightning Damage.
The only thing that limits this is the amount of times I can use Channel Divinity I guess.

But then again, for a core ability in my new set of Tempest friendly Spells, 1d4 feels kinda low in additional damage. Even though I have to agree that when I can use it against all targets of every attack or spell it kinda already surpasses Hex's capabilities. I tried to balance this by not scaling the spells duration with level. 

I think I am going to rework this a bit more anyway. But pushing it to a higher level of spells means not being able to use a core component of my classes kit for a longer time.
Also kinda wanted to do more with the idea of the gods essence being partly infused into the weapon.

I thought I could add unique effects as the spell scales with character (cleric) level.
Like being able to re-roll 1s on the additional damage dice. Or attacking with Advantage if you succeed on a Spellcasting Check against enemy AC.

New Idea:

You can convert your attacks (everything that has an attack roll) to lightning damage, when you crit or signifcantly out-roll their AC.
You can convert your save-based spells to lightning for every creature that fails it's save.

Updated Invoke Holy Weaponry and Storm Strike (previously Lightning Blade)

And added the 3rd level Spell "Storm Surge" an alternate Version of Burning Hands with reduced face-value damage (3d8 vs 5d6 at Spell-Level 3), but an additional 1d8+Spellcasting Modifier damage on the enemies next turn.