Can I listen to Amazon Music offline? from charles hensen's blog

Yes, with Amazon Music Unlimited or Prime, you can download songs, albums, or playlists for offline listening. 

Reference :  Amazon.com/code

Once you have activated it, Amazon Music offers a myriad of features designed to improve the listening experience

• Personalized Recommendations Explore new songs based on the music you listen to.

• Stations and Playlists: Listen to curated playlists and stations that cater to different genres and moods.

• Offline listening: Download songs, albums or playlists to listening offline without internet access.

• High-Quality Audio Enjoy superior audio quality by using Amazon Music HD and spatial audio.

• Podcasts Get access to a huge variety of audiobooks on a range of subjects.

• Integration with Alexa: Control playback with voice commands from devices like your Echo devices.