In my opinion, both of them have the right to exist in English FROM THE GRAMMATICAL POINT OF VIEW. The matter is that the words "animal" or its plural form "animals" are definitions for the word "kingdom". English grammar says that one noun can be a definition for another noun, forming a word expression. Besides, there can be a plural noun which is a definition to another noun, as far as I know, grammar doesn �t forbid such use (we can come that across in scientific articles, for example). So, you can say "animal / animals kingdom" in your spoken language.

Though, "animal kingdom" is a biological term and personally I have never faced "animals kingdom". Being used in special language of science, "animal kingdom" is like a term and, thus, cannot be changed.

I wonder what native speakers will say, �cause I �m not one :)

Still, hope my explanation has sense :))

Best regards

To add to niksailor �s answer: I �m not a grammarian, but it looks to me as if that noun animal is acting as an adjective and that is why it should be singular. Another example may be �the human world, � �the kangaroo enclosure � etc.