Amazon Music Unlimited titles are available for offline playback on the following Amazon Music devices:
Amazon Music for Android
Amazon Music for iOS
Fire tablets (from My Music only)
Important: Amazon Music Unlimited titles can only be accessed and played within the Amazon Music app—they cannot be exported for use on other apps and devices, or copied onto CDs and other external storage.
To access your recent downloads, select Recents from the Amazon Music menu and open the Downloaded option.
Tip: If you're using Amazon Music for iOS, you can also turn on Offline Music Mode under Settings, to show just the music that has been downloaded to your device and is available for offline playback. If you're using Amazon Music for Android, you can go to My Music and select Online Music and toggle to Offline Music.
You are able to download music for offline listening while on the free trial. But you will only be able to listen to your downloads within the Amazon Music app. Depending on which device you're using, the steps I listed above should guide you to your downloaded, offline music so you can listen.