Paula,
It is not an "App" per se, but the Xeno-canto website has many free recordings of Kenya birds. You can also download the MP3s into a collection your smart phone.
If you go to the following web page, zoom in on Kenya, hold the shift key down and drag your cursor to draw a box around Kenya, it will come up with many species hits from the database:
http://www.xeno-canto.org/explore/region