Please try the following:
- Check for updates if any available for your device and update.
- Update Amazon Music app to the latest version.
- Check if the song is queued.
- If the purchased song is showing as downloaded on the Amazon Music app on your device, try deleting the download first. To remove downloaded music on Amazon Music, go to the “Downloads” section of the app and find the song or album you want to delete.
- Once deleted, try restarting the device, open the Amazon Music app and try downloading. You can use the steps detailed here for Android. Check the specific device options on the left side of the page.