It is the same as with all the other sentences so far where the adjective is in front of the noun. The adjective stays singular. Even if it is a question word.
I am not sure "what kinds" is actually correct. Is it?
In practice, with plural nouns, "what kind of" and "what kinds of" are very nearly interchangeable.
I would tend to use "what kinds..." if the things in question come in some distinct types / varieties / species and the meaning is closer to "which kinds". So, all of the following sentences sound normal to me (but they'd also sound fine with "what kind" as well):
What kinds of mushrooms grow in Manitoba?
What kinds of trains can you see there?
What kinds of dogs are in the show?
I would also use "What kinds..." in a question if I wanted to emphasize that I was expecting an answer involving multiple kinds.
"What kind of blankets should we buy?" "Cotton." - sounds fine. We're buying multiple blankets, but only one kind. The question indicates that.
"What kind of blankets should we buy?" "Some green ones and some blue ones." - sounds fine too.
"What kinds of ice cream should we buy?" "Chocolate." - sounds weird. After that, I'd probably reply, "Just one kind? Really?"
And if someone answered "What kinds of mushrooms grow in Manitoba?" with "Delicious ones!" then that would verge on being a joke answer. I'd probably reply, "Haha, yeah, but what kinds?"