venus, Yes, they are correct. any kind of book = a book of any kind ... This is correct any kinds of books = books of any kinds = "any group of kinds" of books....... This is correct any kind of books = books of any kind ........ This is correct any kinds of book = a book of any kinds .... This is unusual but possible. "There are two kinds of book: those that no one reads and those that no one ought to read." H.L. Mencken (famous American essayist)

Kid: What kind of book can I have? Dad:Any kind of book is OK. Since any kind is OK, it can refer to just one kind, or two kinds, etc. Think about it.

"any kind of book" is correct, eg I like any kind/type of book Or I like different kinds of books

As the emphasis is on “any kind of”, it is quite natural to use it with singular uncountable nouns. So “any kind of book” would be correct.