When using Airplay to beam Amazon Prime Instant from iPhone to Apple TV 4 there is no sound but perfect video. The only way I can provide a workaround is to use screen mirroring then the sound comes through.
I tried it and if I AirPlay first through control center, I didn't get any audio. If I instead used Amazons AirPlay button, I got stereo sound. Pretty sure you can't get 5.1 over AirPlay
I get the opposite with iPad to my AppleTV 3 - sound but no picture and if I turn on mirroring I get a black screen.
I thought maybe Amazon has deliberately broken it as everything else works fine but it sounds like it should work, which is encouraging