It's like Iva said: "what" is used to ask when there are an unknown number or infinite possibilities for an answer, and "which" is used if you are choosing between a more limited number of (already defined) items. In Czech, "jaký" means "what kind", and "který" means "which".
Good question... it seems that when you use "which kind", you usually have several options from which you pick :)... like "which kind of ice cream would you like?" but you wouldn't say "which kind of person would do that?!" but rather "what kind of person...". I agree there's probably a grey zone in which both can be imagined... in this case I am more inclined to "what", because it's a general question with no specific pre-offered kinds.