One of the campaigns I'm participating in (currently on summer hiatus tho) has got swashbuckling action on flying ships, cannonades, and artificer wet dreams. But the question on how to buff the ol' fighter class so as to not diminish the role of this core of classes. Well, after looking at a variety of pundits and variations, we've come up with a simple but effective version of a gunslinger fighter.

So (1): Set up a class of weapons called Firearms and define what types are available. In the setting we're using flintlocks are common and pepperbox weapons are very rare. The DMG does most of the work on setting up weapon damage and ranges already. Missfires happen on a natural 1 or 2 unless you are a Fighter with Firearms training or the Gunsmith Artificer from TCE

Fighters get the option Fighting Style: Firearms

You gain +2 bonus using Firearms and Firearms only misfire on a natural 1 (they misfire/jam on 1 or a 2 for someone proficient with them, 1-3 for someone not proficient). You can take a move action to clear the jam.

Now (2) Fighters get the option of becoming a Gunslinger. A fighter that lives, breathes, and (often) dies by the gun.

Subclass: Gunslinger

Critical Shot: Beginning when you choose this archetype at 3rd level, your firearms attacks score a critical hit on a roll of 19 or 20. You also gain a +1 to initiative rolls when using a firearm. Missfires only occur on a Natural 1.

Rapid Fire: At 3rd level, if you are using a multi shot firearm or two pistols, you can take a bonus attack per round with them.

Rapid Reload: At 7th level, you can take a free action to reload your weapon or swap out with another loaded firearm on your person. Note the reload option is only if pepper-box or revolvers exist in your setting, otherwise it's weapon swap a la Pirates of the Caribbean

Bleed out: Beginning at 10th level your bullets do more lethal damage. Whenever you get a critical hit, the wound causes the target to bleed out a d6 per round unless they make a Fortitude save to resist your expert marksmanship. The saving throw DC is calculated as follows:

Bleed Out save DC = 8 + your proficiency bonus + your Dexterity modifier

Note: Bleeding Out is a condition and can be stopped by Lesser Restoration or any Heal Wounds type of spell of lvl 3 or higher

Expert Shot: Starting at 15th level your firearm attacks score a critical hit on a roll of 18 - 20 and your shots cause a bleed out of d8 per round instead on a failed Fortitude Check.

Deadshot: At 18th level you can take a -10 modifier to do +10 damage on a target. This can be made with multiple shots and also stacks with critical hits. Additionally the damage per round on a bleed out is now d10 hit points.

Of course you can now add on magic bullets and guns to make your gunslinger more bad ass.

Hellbore Rifle: A +1 flintlock, bullets fired from it also do 2 points burning damage and it can fire, up to 6 shots per day, bullets that act as Scorching Ray.

Ghost Pistol: A +1 pepperbox pistol, can load up to seven shots. Bullets fired from this skull blazened wreathed in black energy pistol do necrotic damage and on a critical hit heals the wielder d6 hp.