When will the Apple TV+ be available in Kenya?

Unknown, until Apple makes an announcement about that.

Availability of Apple Media Services - Apple Support

I have gotten 1year apple tv subscription with the purchase of an apple device. The app doesn’t work in kenya. I have attached a screenshot of what the app shows. How am I supposed to use the apple tv subscription.

Apple Tv + is not available in that location. You will only be able to view synced videos (videos transferred from computer to IOS device) via the TV app.