"What kind of car do we use chemical for?" is a strange sentence. First, you are missing an article before the word 'chemical'. Second, it doesn't make sense without more context. Why would we want to use a chemical for a car? Do you mean a chemical to use to clean the car or a chemical to use as fuel? In either case, the word 'chemical' is too general and vague to convey much meaning by itself.

Based on the sentence you wrote this may be correct: On what kind of car do we use this chemical?

The sentence is incorrect because it is incomplete. So, you could say, 'What kind of car do we use this chemical on?' Secondly, the sentence doesn't really make any sense even though my version is grammatically correct. You need to give more information.