Updated 5-21-2017

Amazon's music streams are encrypted. They cannot be downloaded. HOWEVER, now with Replay Music 2.0 you can use the new audio capture mode to record any audio that is playing on your Mac. Including Amazon Prime Music. Here's how:

  1. Open Replay Music
  2. Switch on monitoring from the bottom-left of the main window:
  3. Select Audio Capture Mode from the bottom-right of the main window:
  4. Open Amazon Music
  5. Increase your volume level to at least half and don't change it while recording. Do not mute your audio or lower the volume. Do not play any other audio or system sounds as they may be recorded as well.
  6. Play the song in Amazon that you want to record. Replay Music will record it as it plays. And will automatically split and tag the tracks for you.