I don't claim to understand the tectonic environment there. Kilimanjaro's peak is actually in Tanzania, and located nearby is Ol Doinyo Lengai, the world's weirdest volcano. Kenya and Kilimanjaro are both located to the east of the eastern Rift Valley. Nice map -- look how Ol Doinyo Lengai, Nyamulagira, and Nyiragongo are right in the Rift Valleys:
I would hazard a guess that the volcanism there has some similarities to the environment in Iceland, which is also sits on top of a spreading center. But I don't know how shield volcanoes interact with spreading centers.