I don't know if I agree that "Elephants do not like rice" is a reasonable alternate translation. It seems like you would only use 'kein-' if you would use an indefinite article (ein-) in the positive. But you would never say, "Elephanten moegen einen Reis". It would be "Elephanten moegen Reis/Elephanten moegen Reis nicht". I understand that Duolingo is likely just trying to get us to use 'kein-' in the singular masculine accusative, but it may not be helpful in the long run. Am I crazy?
Both "Elefanten mögen keinen Reis" and "Elefanten mögen Reis nicht" are fine. Personally, I prefer the former.
I can understand how you might think that, but it's just not true that "kein" is only used where "ein" could be used. On the contrary, it's quite common to use "kein" in combination with mass nouns, and negating nouns with "kein" rather than "nicht" is generally considered more eloquent. A couple of further examples would be "Sie mag keine Musik" and "Sie haben kein Wasser".