This is a bug report for the Amazon Prime tvOS video app. I'm running the app on Apple TV 4K. I have isolated the issue to the Prime app - no other video streaming app is affected.
The issue is that audio is out-of-sync when Frame Rate Matching is enabled on the Apple TV. Disabling Frame Rate Matching resolves the issue, however the benefits of this feature are then lost and the video stutters as a result. The issue does not occur on other streaming apps such as Netflix.
Resetting and/or restoring the Apple TV does not resolve the issue. There are other user reports for this issue on Reddit - several threads mention the issue, here is one example:
outpost33 is right. Disabling “Match Frame Rate” in the Apple TV settings is not a solution because this introduces video flickering.
Btw. this bug seems to be limited to AirPlay audio and when sending audio via AirPlay to an external receiver, not when listening audio via HDMI on the TV speaker. This issue also seems to be limited to 50 Hz output and 24p or 30p content (23.98/29.97 fps).