I'm wondering if any other prime members are having the same problem as me with accessing Prime Music.
I can't play prime music via the Amazon Music app on my android smartphone. Instead the Amazon Music app links to Amazon Music Unlimited - with a £7.99 per month fee unless you cancel that (which I have done).
I had a very long chat with customer services (over an hour !), involving lots of deleting and reinstalling the app, etc. and they said they've forwarded the issue to investigated further....
The cancelled Amazon Music Unlimited subscription on my account runs out in early November, so by then I hope Amazon will have sorted it - otherwise presumably I won't have any Amazon music available on my smartphone.
I never had any problems until they introduced "Amazon Music Unlimited".