Turn 1: Create an AOE cone that is DEX save for 2d8 or take half. 
Enemy Turn: Must make save again, or same damage.
Turn 2: Make the damage happen... again? 
Enemy Turn: Same
Turn 3: Again...

So with a level 1 spell you're doing potentially 10d8 damage in a 25ft cone. 

You might be better off basing the spell on Witch Bolt, and making a Fire version of it. A continued effect damaging spell exists, and is balanced. One target -> Attack roll, damage on success, then repeat damage roll as an action on your turn if you maintain Concentration.

I think you might want to check your Math there.   10d8 isn’t possible.  Maybe 6d8 if you keep an enemy in the cone for all three turns, and they fail all the dex saves.  

Anyways, this lets someone deal a good amount of continuous damage without it being too powerful, have reasonable limits and flexibility.  For instance, it’s possible to get enemies into the cone later as your using flamethrower.   Hence damage would need to be rolled independently as well as saves.

Quote from kraziboidemonking >>

I think you might want to check your Math there.   10d8 isn’t possible.  Maybe 6d8 if you keep an enemy in the cone for all three turns, and they fail all the dex saves.  

 

Anyways, this lets someone deal a good amount of continuous damage without it being too powerful, have reasonable limits and flexibility.  For instance, it’s possible to get enemies into the cone later as your using flamethrower.   Hence damage would need to be rolled independently as well as saves.

Also important to note that if any of your party members can shove an enemy into your cone, you can suddenly add a new enemy to do damage to at the start of your turn where, once again, Witch Bolt is relegated to a single target.

So your max total damage for Witch Bolt is 10d12 (or 120), maintaining concentration, and dedicating your action to the spell (aka not able to cast other spells, or attack, etc.) If you miss your attack the first time? Zero, zilch, zip. Max: 120 damage over 10 rounds (1 minute), no action allowed

Your max total damage on this spell is 6d8, BUT even if everyone saves the first round, the effect maintains, repeating a chance at damage as the spell goes on. In addition, its a 25ft cone, meaning you have a max potential of 5 targets IN THE INITIAL LINE, killer in a horde. Doesn't even include the radial off that cone, which gets insane. You'll have five squares up, then five squares at the end line, so you're already at 9 squares there. Pretty sure you're at 15 squares total.

In that case you have a middle potential damage output of this spell as 6d8 * 5, which would be 30d8. (or 240) for 5 targets, or 45d8 (360) if you're firing on a horde (all squares filled is 15 squares), double or more a spell that has a chance of outright failure from the get-go, and you only have to maintain concentration for 2 subsequent turns, and you don't have to waste your action on it. Max: 240-360 damage over 3 rounds based on mid-cone (5) and full cone (15), action allowed

Ooh, also good to note: No half damage for Witch Bolt, whereas you're guaranteed to do SOME damage with this. Having used Witch Bolt heavily in a recent campaign I'll get snake bitten and burn my spell slots, this one is crazy since I can do three rounds of AT LEAST half damage, to 1-15 creatures. I hope you're catching my drift here, since this is a cool idea - you just need to scale with the game that exists, not create a whole new power level. Anytime a piece of homebrew comes around where you would pretty much always pick that, instead of something RAW because it's so good... It might be too good ;)

Well it was accepted as a level one spell, so it would seem others disagree.   For example, the fact that the spell ends if concentration is broken.  Additionally, it can still affect allies as well as enemies.  If you use Witch Bolt, it’s only a single target, but with this if you get something that can shoot tentacles out and grapple an enemy and pull them in, you burn them too.  

And incidentally there is the simple simple fact dice rolls are important here.   With Flamethrower you can’t roll a bat 20 to enhance damage, but Witchbolt you can.   Besides, there is a similar non-concentration spell called burning hands.   In fact, burning hands does more total damage.

And I don’t think it’s likely for any DND campaign to get the sheer lucky roll you suggested.  

And I find it strange you mention what happens if they pass the first time and fail the others, and not the inverse where they fail the first but pass the others.  

So, there we go.   Established there are level one spells that do higher damage, and concentration spells that don’t risk hitting allies, and the simple matter of the fact that dice rolls can determine everything.  After all, half the damage of witch bolt that you keep mentioning is 6, and half of the total damage of Flamethrower is 8.   That’s just a two damage difference of an average.

and of course, it takes up your concentration so unless my brain has totally fluked, you can’t use another concentration spell at the same time.

So given all that, and considering it was accepted, I would have to disagree.

Witch Bolt can't do half damage (unless resistance), dog. Your spell has guaranteed damage, since it does damage on a successful save. Witch Bolt could fail the attack roll, and then it is a 100% wasted spell slot. If you do crit with Witch Bolt, it only doubles the damage die on the first hit, not on the sustained damage - which again requires your action. Witch bolt is ALSO a Concentration spell which you have to maintain concentration on for *10 rounds* instead of 3, if you hit the first time. 

There are no level ones that have the damage potential of this spell, because nothing has the 25 foot cone and sustained damage as this attack. You mention Burning Hands which is a **15 foot cone** aka max of 6 targets, for one hit of 3d6, half on successful save. Minimum damage for that is 3. You can do 6 per target. Rolling all 1s, successful saves. (Half damage always minimum of 1)

This takes concentration, but only 2 rounds after the casting. Not hard to maintain concentration, esp. since any caster should have Con as their 2nd highest score after their casting stat. Only taking massive damage makes concentrating hard -- or, casting another concentration spell.

But since, unlike Witch bolt, you can use your action for something else while this spell is up, you could cast ANY spell that's not concentration (heck, follow this up with burning hands, why not?), or attack, or do any number of things. Witch Bolt requires the action, so you can't cast spells unless they're bonus action, of which there are very few choices AND most bonus action spells are Constitution or are for Rangers/Paladins.

Also dog, they accept anything homebrew that doesn't break the rules, doesn't mean it's balanced. Take a browse my friend. I've done unbalanced homebrew, I've done stuff on here, gotten notes and put out new versions. And the thing that makes homebrew better is balancing against notes and against stuff that exists in RAW. 

But here's the thing, you do you. Obviously it's no skin off my back, since I personally would not allow the spell in my campaigns, so your assuredness in this design does not matter... I just like to give reasons to people when I leave a downvote on something, since that seems more helpful than just clicking an arrow. 

Enjoy your homebrewing, this and the future, and enjoy the use of it in your campaigns! I feel I have explained as best I can my thoughts, and as we disagree I can no longer assist in balancing this, so I'll leave you to it. 

Ok. So we went on a quest and found magical wolves that basically are bags of holding so we're wondering if we filled one with gasoline or any flammable gas and use one of our fire spells or lighters and have him spew out gas and light it would that count as a flamethrower? (lets say he's eaten a ridiculous amount of gas).

Late to the party, but also not a fan. Durations between 1 and 10 rounds are generally too finicky to be worth attempting, if the the intention is a multi-round attack it should be 1 min. The range is also probably messed up. 25 ft range and a 25ft cone means you can hit targets 50 feet away, from the descriptive text that doesn't seem to be your intention. 

Comments around this spell seem to suggest it creates a "damage zone" like flaming sphere. If that's the case, it needs some language to indicate when the save is triggered. If instead it needs to be retriggered each round you'll need to indicate the action costs, that'd be more comparable to dragon's breath from Xanathar's guide.

I'm compelled to point out though, both of these comparisons are to 2nd level spells. A 25ft cone is larger than either spell area by a solid margin. 2d8 is solidly "middle of the pack" between Breath's 3d6 and Sphere's 2d6. In the case of Breath, it's obviously a result of the bonus-action cost upkeep vs sphere's triggered zone. In either case, you should drop the damage to a single die if you're keeping this at 1st level.