[antlane]

Try: Keep the AVR powered on, restart the FireTV, make sure the FireTV is plugged into the AMP and _not_ into the TV.
Then: start kodi, enable debug logging there. Quite kodi, start kodi again and now post the Debug Log

Not funny, btw. I currently have no idea what is going on there. Might be some fucked up ARC setting, but let's find out.

Here's the new debug log having followed your instructions (apart from quitting Kodi and starting again as debug logging was already enabled).
https://paste.kodi.tv/aroqaqayuw.kodi

FireTV is plugged into the amp and the amp is connected to my TV via ARC.  I've just tried plugging the amp into a non-ARC HDMI on the TV (and restarted the FireTV with the amp remaining on) but it didn't help.  In case this shows something different on the logs, here they are:
https://paste.kodi.tv/umovixumon.kodi

Sorry to be causing you such problems!