I don't think Black Zetsu will end up betraying Kaguya. Another betrayal would show lack of writing skills right now, plus I don't think Masashi Kishimoto will repeat himself in such a short span of time. But then again, we never know.
I for one believe that the key to defeating Kaguya lies within Black Zetsu. I think her actual power comes from the Zetsu part. See it like this: When Hagoromo and Hamura sealed her she created Black Zetsu as a physical manifestation of her power/chakra/will so that even though she wasn't around, her essence and power could plot to bring her back. Therefore, defeating Black Zetsu will weaken Kaguya.
Just a theory.