Haven’t followed the exact custody of Zanzibar, but A. It’s not *in* Kenya, geographically (island), and B. It belongs to Tanzania. Mostly muslim.
It’s the place Hitler, at an early stage before he had fully conferred with Hajj Amin, claimed to want to send the Jews.
The issue has been not the custody of Zanzibar, but the custody of Mombasa, which seems to have been kind of "shared" between Kenya and Zanzibar.
Zanzibar at some point joined up with Tanganyika to become Tan-zani-a. Presumably after 1963.