For anyone else landing on this page: to make it stop I think you just need to revoke the Microphone access for the Amazon app. I think they have a glitchy implementation of microphone use.
Probably checking that mic access really works when the app starts so it knows whether to show you a mic icon in the search. I know I’ve had it make my music sound like a voice call when I launched it in my car, and then it switched back to normal sound when I left the app.
I’ve used voice search maybe two times since they asked me to enable it, so no loss for me to prevent it from pausing my music randomly.