I was there a couple of months ago on a medical trip. As far as I could gather, there is no legal hunting in Kenya. There is also no private gun ownership in the country. Interestingly (on a trad archery note), the guards at the hospital I was working at stood sentry with a self-bow and a cowhide quiver with about 8 or so arrows with a nasty looking "trade point" attached. They had a short sword for the close in work. Maybe I could post some pics later if I can locate them and anyone is interested.
There are some fantastic areas to view Kenya's abundant wildlife with the best possibly being the Masai Mara. This is the northernmost tip of the Serengeti. The Aberdares and it's signature hotel, The Ark, can also be interesting if the animals are active.