Perhaps if you went into detail about what you wanted the character to do and be like?Ok, sorta looking at the Clint Eastwood Spaghetti Western of a man great with a gun that likes to throw dynamite around.
Thomas
Sort of like James Coburn's character John Mallory in "Duck, You Sucker" or "A Fistful of Dynamite."
In case you're unfamiliar with Sergio Leone's lesser known western (it takes place during the Mexican Revolution...) His character is a demolitions expert who also happens to know how to use and uses guns...though he primarily relies on his clever use of explosives- deferring more of the gun play to his partner. I'd recommend it, though not as highly as "The Good, The Bad, and The Ugly" or even "The Good, The Bad, and The Weird," for that matter.In any case, I'd sooner build it like that, an explosives nut than The Man With No Name...not to say I wouldn't, or haven't already based a character on Clint Eastwood's reprising role...(Earth Genasi nicknamed Flint Weststone...I know. It was an Alias, not his actual name, even that was Marble Forge- which of course made him a blacksmith. Being from the one place in Faerun with guns, he had one, as little as he got to use it.)
Flavor-wise, from what I can tell- you're more Gunslinger than Alchemist (which is more Alchemist than Demolitions expert).
Now, mechanically speaking...
Int is your ability score after Dex take a decent Wisdom for Grit (since you aren't starting with Extra Grit, you may want to take it later).
I'd probably choose which one you'd want more of or go an even split. If flavor wise you want more gunslinger, you should go more gunslinger with a dip or two in Alchemist. Depending on level of course. I'd probably go Alchemist 1/Gunslinger 2 for a Clint Eastwood if I were you, if I were me and doing James Coburn I'd do it the opposite (Alchemist2/Gunslinger1) for openers. Human of course. In either case. I'd probably start the 2nd level of Alchemist with "Delayed bomb" so you can have a longer "fuse," then follow with "Explosive Bomb" or "Concussive Bomb" if going to Alchemist 4.
I'd go gunslinger at least 4- probably 5- levels down the line- probably ending up 4/4 at some point before going 5/4 and furthering that gap as necessary. From the sound of your inclinations I'd say that you probably want to make Alchemist your low class...maybe end up something like 6/4 Gunslinger/Alchemist. If you get that far. For survivability you'd want to have more gunslinger anyway, not that the skill points of the Alchemist aren't tasty.
For Gunslinger, deeds of choice- for Clint Eastwood, would be Deadeye and Gunslinger Initiative. Feat choice after your first two is up in the air, but if you don't get access to Advanced Fire Arms burn up Extra Grit for Quick Clear and/or take Rapid Reload to increase your action economy.
As far as Skills. This build would be very Craft heavy, and yes Craft Alchemy would be a useful overlap. Knowledge Arcana and Engineering would be good choices, good perception and stealth would help. Survival is a nice overlap. Handle Animal and Ride if you've got both the skill points and the horse. Otherwise avoid it.
I do think that you'd probably be better off sticking with Gunslinger and just stocking up on Alchemist's Fire, not that it wouldn't work to some advantages to multiclass, it's just more James Coburn's character to go Alchemist than Clint Eastwood's.
Apart from Craft Alchemy and theoretically making explosive or extract infused rounds, there isn't much use in multiclassing much into Alchemist if your goal is a Gunslinger who also happens to sling dynamite on occassion, often would be different, and you'd have to improve the bomb as you went maybe going 5/5 just to get 3d6 Bomb.
It's a shame that there isn't an Alchemist archtype that just deals with explosives.
Hopefully in the Ultimate Combat?