Access to my Amazon music on Apple Watch

It is available now. I am using it and it works well.

I just upgraded my iPhone Xs to a 13. I had to reset the watch because the store didn’t unpair the old phone from my watch. Once I did that by resetting the watch, I paired the new phone and the watch. I had to install the Amazon Music app on the watch again. This time, there was a complete url and an alpha numeric PIN. I followed the link using Safari on my phone. Then I entered the PIN when requested. It worked after that. I hope that description of the steps I took will help you. One question: This may be immaterial, but have you updated your phone to iOS 15? That may be immaterial, but I have updated to iOS 15.2. If you are running an older version, could that explain the difference between your experience and mine?