Amazon working on Amazon Music app for Windows devices | WMPoweruser
That could be something...
I hope it's true. Prime memberships have been getting better and better lately.
You can play Prime Music on most devices that support Amazon Music, including Kindle Fire HD and HDX, iOS devices, Android smartphones and tablets (v. 4.0 and above), Amazon Music for PC and Mac, and the Amazon.com website. I'm sorry Prime Music is not supported on any other devices, including your Window's phone at this time with no expected time frame either.