The table suggests they have Improved Evasion, but not in the rules text and they never get plain Evasion.
I don't see a HD anywhere.
They're lawful, but they have a creed of action? I'll admit to disliking Steven King, but the creed is also unclear in meaning. Perhaps it's just a concentration aid, and could thus be split up into the ability names to give flavor?
I'd move some of the later abilities (Know Your Shot, etc.) down but give them Concentration or firearms checks.
Fan the Hammer is a massive timewaster- roll six attacks, a limited number of times per day? I can see it being ridiculous with Vorpal bullets or something (CHAINSAW BULLETS) but it's still nonsensical and odd. Change it to something that allows a Flurry, or an improved version of same.
It's quite restrictive in role and has little that is attractive in the higher levels.

Suggested Changes: Give an increased chance or guarantee of finding a Legacy Weapon with the feats paid off. Write up several different legacy weapons to go with the class- six or seven should be sufficient. This allows a few different styles to develop while retaining the feeling of SHOOTAN MANS. These don't have to be singular items; perhaps any sufficiently fated person of this class could make one given time and gar. In addition, change out all the free feats for bonus feat slots, and drop more in the higher levels.
Separately, there's already a system for enchanting items on the fly- Give them a cut-down version of artificer Infusions, along with a substitute for Action Points (or if you use action points, those). Of course, you'll need some unique ones to make things fun... (Name On The Bullet?)

>> The table suggests they have Improved Evasion, but not in the rules text and they never get plain Evasion.

My fault. Updated.

>>I don't see a HD anywhere.

Updated.

>> They're lawful, but they have a creed of action? I'll admit to disliking Steven King, but the creed is also unclear in meaning. Perhaps it's just a concentration aid, and could thus be split up into the ability names to give flavor?
>> I'll change the alignment. The Creed is similar to a mantra to focus the Gunslinger's energy.

>> I'd move some of the later abilities (Know Your Shot, etc.) down but give them Concentration or firearms checks.

Will try to work on balance.

>> Fan the Hammer is a massive timewaster- roll six attacks, a limited number of times per day? I can see it being ridiculous with Vorpal bullets or something (CHAINSAW BULLETS) but it's still nonsensical and odd. Change it to something that allows a Flurry, or an improved version of same.

I imagined it as like burst of damage, 6d8+6xmodifiers. Also, if the Gunslinger had taken the precaution to load his revolver with enchanted bullets, he could potentially have a large and variable effect on the target.
It's quite restrictive in role and has little that is attractive in the higher levels. I'll compare it with the Monk's FoB, but I actually like this feature.

Legacy weapons sound like an interesting idea. I had originally considered having the guns unable to be enchanted even though magically (because of interfering magic or some explanation), but perhaps with legacy weapons, each with a different style like you said. THe class was actually made for a guy that is newish to DnD and I wanted to make a class that was more than just 'I hit him with my axe'.