I sent a message from the Amazon Music app on my iPhone asking if there’s documentation for their API. This was specifically for a Volumio plug-in.
On a related note, I’m using airplay from my phone to play Amazon Music through Volumio. It’s not as seamless as I’d like but it works reasonably well until a plug-in can be sorted out.
On another related note, I found an Amazon Music Github project a while back. I’ll see if I can dig it up and post a link.