Please make sure the app has the necessary permissions on you smartphone: Settings> Apps> Amazon Music>Storage.
- Check again your plan, Amazon Music Free provides free includes ads. Go to Your Amazon Music Settings.
- Open the app store you used to install the app on your device.
- Search for the app, and open the app’s detail page.
- If an update is available, an Update option displays.
- Make sure you clicked on the download app’s button Download Amazon Music Playlists for Offline Playback