Q: Does anyone know how to set up amazon prime play on Apple TV?

This is a limitation of the Amazon Prime Video application, they did not enable video over airplay - just audio.

Not possible.  Amazon has blocked all Apple users from this technology due to politics and Money. Nothing is wrong with your device, we all need to petition Apple to extend the olive leaf to Amazon and come up with a way so Apple customers can access Amazon Prime Videos.  For now we are all blocked!

They have supposedly enabled video Airplay now - is your video app up to date?

http://techcrunch.com/2013/09/17/amazons-instant-video-app-adds-airplay-support- for-streaming-to-apple-tv/