From my study of the matter in Uni and paper on same, I don't think it is correct to say that
Britain
was "kicked out" of Kenya in any sense; this was the time of colonial disengagement and the two more or less coincided.
The Mau Mau if they were ever much more than gangsters swiftly degenerated into same and their suppression was a notable counter-insurgency success along the lines of the Malayan "Emergency". Certainly some land policies in Kenya exacerbated the problem, as much as Kikuyu population growth did.
Not a few parts of Africa would be very glad if they could return to the peace, order and good government of that per-independence period. Self-government is a fine thing, but decades of anarchy, corruption and brutal repression can take the bloom off that rose quite effectively.