I was curious how well a Fighter (Samurai) Artificer (Alchemist) would work

I'll start off by saying that most anything can "work." If it's what you want to do and your party isn't big on optimization, go for it. Thematically it's a very unusual combo which could provide some interesting roleplay and out-of-combat options. Mechanically though, there is little to no synergy here and what you lose in terms of damage/AC/stats does not make up for what you gain in terms of effectiveness in combat (and even out of it as your ability scores are going to be spread a bit thin to make the most of either class).

As a fighter, multiclassing out means you get your extra attacks and other features later. Your job is to hit things with your weapon as many times as you can.

As an alchemist, multiclassing out means you get spells and infusions later. Alchemists are the "caster" subclass of Artificer and typically stand back and use cantrips. They also need to be holding their alchemist tools to make use of their level 6 feature, which doesn't work well with fighter.

Pretty much the only thing from Alchemist that helps the fighter is the ability to make your own +1 weapon or armor, and I suppose you can drink your own elixirs, although spending your action to do it is a steep cost.

And this is a good place to segue into the sad fact that Alchemist is just not a good subclass even when you're not multiclassing. It has multiple issues and just doesn't keep up with the other Artificer subs. But the main issue here is that Samurais and Alchemists are just built to approach combat in completely different ways.

What you do gain is some versatility. In a given battle, you can behave as a samurai or an alchemist. But you will perform as a very underleveled version of either of those. Ideally a multiclass provides you with features that work together in addition to providing a few new options. This is not that.

I think perhaps Armourer would make a better Artificer subclass to go with a Fighter.

The problem is that you're trying to be an air-droppable tank. A tank that can be dropped into coat sounds great in theory, but in practice...it's terrible. What makes it good at one role makes it terrible at the other and vice versa. To be air-droppable, you have to be light and small. That makes for a crap tank. To be a good tank, you need to be heavily armed and armoured, which makes for terrible transport on a plane and to parachute. What you end up with is something that can do kind of do both but is terrible at either role. That's why we don't really have them anymore.

Multclassing has similar problems when you mash things together that don't compliment each other. You end up with something that sucks at both roles. When you choose your second class, it's best to choose one that has brings you something that in someway replaces what you lose by not progressing in your primary class. A Fighter Archer that gains a levels in Rogue to get Sneak Attack can be awesome as an example of what might work as a multiclass. 

The thing is, you're sacrificing your Fighter abilities that let you tank and deal out attacks for...the ability to infuse and to make elixirs etc? They don't really help with your role and it seems like you're trying to almost play two characters at once. That's probably the way that I'd put it. Assuming that you're doing 50:50, at level 20, you'll essentially be getting to pick each turn to be a L10 Fighter OR a L10 Artificer. While fighting creatures designed to challenge you at L20. It's not quite that bad since you still get L20 HP, but effectively that's what will be happening.

If you're all about roleplay and will enjoy it, crack on! Nothing wrong with that at all. So long as you're having fun, then that's what's important. I just don't want you to get to L8, playing with the equivalent of a L4, and resent your character because he just can't keep up in combat. The further you get, the less likely that you can grab the spotlight with some cool move because you're fighting  with lower level moves than the rest of the party.

If you do decide to take this unusual multi class that suffers from the problems identified above, I think you can ameliorate the issues a bit by choosing a Fighter subclass that at least benefits from INT, as your Artificer needs high INT.  That’s Eldritch Knight and Psi Warrior.  

I think this build would also benefit by trying to maximize use of either Green Flame Blade or Booming Blade in combat.  Make sure you infuse your melee weapon or shield so you can use it as a focus.  Most of the time, your spell slots will be better for control and support at the lower relative levels.

Finally, if this is a few level dip only, it will make more sense for you to be mostly Fighter.  Artificer generally, and Alchemist specifically, gets something at every level through 11 that makes multiclassing less rewarding.  And Alchemists generally shouldn’t be melee combatants, so they usually don’t get much from levels of Fighter.  But a few levels of Artificer for support options and infusions could make sense for an Eldritch Knight, especially if it’s a low magic campaign.

The biggest problem with this combo is that the classes' best features are inherently incompatible. A samurai's Fighting Spirit can only be applied to Weapon Attacks, while the Alchemists's Alchemical Savant ability only applies to spells made using your alchemist's supplies as a focus.

If you want to be a Samurai who has access to a variety of potions, I'd instead recommend taking a Background that grants you proficiency in Alchemist's Supplies. You won't get the free random potions each day that Alchemist grants, but you'll still have the ability to craft potions and if you use it creatively you can work with your DM to create some fun, interesting stuff.

Hey guys, Do you have any idea what my friend would benefit with with her build she'll drop it in in a minute...

Hi, the multi class build is this:

Ranger (Hunter) 5, Monk (Four elements) 5, Fighter (Champion) 5, and Rogue (Assassin) 5.

Any ideas how to most efficiently use this???

Any specific weapons or magic items or ways to roleplay???

Thanks...

What was your current weapon loadout again Luna???

Attacks or weapons???

WEAPONS!

Scimitar of sharpness and scimitar of speed...

Oh and the chill touch and the flurry of blows, does that count?

Can someone help us rebuild how to use this character more efficiently??? Also how to roleplay???