I like the idea of a Chemist in the game, but from what i see from the Skills you listed, is just a fancy AST with the fairy gauge from SCH. I have some idea's to share on this as well, but i have to apologize in advance since i never played a final fantasy game before that includes chemists so the stuff i mention might not be accurate or do justice for it.

From what i see in the Wiki's, a chemist focuses on mixing potions while using daggers, firearms or rods as their weapon.
I think a Chemist should have the ability to improve the utility Potions from a Alchemist for his own use, why? because chemistry is the evolved form of alchemy. Stuff like turning a Potion of Paralyze into a AoE Bomb and doing some damage or allowing Healing Potions to change some properties, like doubling its effect while having a low chance for "sideeffects" that can happen at random which are both good and bad could keep this interesting (like granting a berserk status along with blind for a party member, like mentioned before, with a low chance of happening of course). As for which Weapon to use, i would say using a small firearm or dagger would be a better idea than a rod, for i would expect a chemist to coat his dagger or the ammunition with ailments or properties which could work for a limited amount of hits/time.