If I understand what the question is (and forgive me if I’m misinterperating things) it sounds like you want to use Explosive Missile with the Rapid Reload/Quick Draw abilities.

The short answer is, you can’t. Sorry. But don’t dismay! There’s a lot the Alchemist can do otherwise.

The long answer requires a bit of explaining, which I’m going to do for the benefit of readers, who may not know what’s going on here (I’m sure you do, but many don’t, plus I like flexing my design/rules muscles):

Alchemist Bombs: As a Standard Action, the Alchemist draws, combines, and throws a bomb. He’s obviously not going to keep active explosive chemicals strapped to his body, so he has to properly mix them before they can be a bomb. This is why bombs require a Standard Action to throw just one. At Alchemist level 8, he can take the Fast Bombs Discovery, which lets him throw a number of bombs equal to his number of attacks as a Full-Round Action.

Quick Draw: There are several things about this feat that many people miss. It only applies to weapons, not potions, scrolls, wands, or abilities like extracts or bombs. An Alchemist with Quick Draw is still limited to the bomb ability’s restrictions. There is a reason for an Alchemist to take this feat though (see below).

Rapid Reload: This feat lets a character with a firearm or crossbow reload those weapons faster and can eventually get them to a speed of loading fast enough to use those weapons with a Full-Round Action. Rapid Reload can’t be used in conjunction with Explosive Missile.

Explosive Missile: Now, this ability lets the Alchemist infuse his bomb’s damage to a single piece of ammo and fire it, all as a Standard Action. Because it’s its own ability, Quick Draw and Fast Bombs don’t apply. Also, Fast Bombs doesn’t apply to this ability. Like Vital Strike, and other abilities of a similar set-up, it exists on its own and can’t be used in conjunction with some of the other abilities.

Now, as an Alchemist, what does this all mean? It means a couple things. The first is that their bombs are a special ability, exempt from the rules related to mundane weapons, but they have their own special features that make them great. They’re eventually an insane source of damage and can create control circumstances.

The second is that using a regular ranged weapon as an Alchemist should be used alongside bombs, but it can’t be used in same turn as bombs. They’re a great fallback and alternative to bombs, since bombs can run out (and I don’t know any GM that takes keeping track of ammo seriously).

Third is that Quick Draw in relation to bombs is useless. However, Quick Draw has its uses. Since Alchemists have Throw Anything, they can literally throw anything in their pockets at an enemy. Normally, you can only throw mundane items once-per-turn, but with this feat, you can throw multiple things as a Full-Round Action. So, with Throw Anything and Quick Draw, you can literally throw tons of stuff at the enemy. Part of being an Alchemist is being a one-stop-shop for all things item, with Throw Anything, you’re also the one-stop-shop for throwing random drops from monsters/dungeons at anything. Got a bunch of daggers, longswords, maces, clubs, halfling slings, coins, and/or crystalized dog poop the axe-based Fighter can’t use? Well, Throw Anything allows you to throw them all!

So, to sum up, most of the things in your question work on their own, but can’t really be combined. I’d pick either Rapid Reload or Quick Draw, depending on the style of Alchemist, throwing lots of random things or shooting lots of things.

I’d say that you should probably not dip into Fighter. The only time I’d consider doing that as an Alchemist is to get heavy armor for a Two-Weapon Fighter melee/ranged Alchemist. That is, an Alchemist that’s using something like two kukris in melee while using bombs at range, as Alchemist abilities are not affected by armor at all. Otherwise, you slow down the power of your bombs, the number of extracts you can have, and in the long run you lose your Grand Discovery.

I hope this helped and was informative!