If you're referring to tracks included with Amazon Music, and your iPod is an iPod Touch running ios 11.0 or higher, you can install the Amazon Music app from the app store on your device, then download your music.
If you're referring to purchased songs or albums, you can add those tracks to iTunes from a computer where you have downloaded your purchases by following these steps:
Open the iTunes app.
Select Add File to Library from the menu.
Browse to the file or location where you saved your download (e.g. your default "Downloads" folder, "Your Music," your "Desktop").
Select each track you want to add and confirm.
You can also set up your Amazon Music app on PC or Mac to automatically export all your downloads.
Open the dropdown menu in the upper right corner of the application window.
Select Preferences and scroll to the "Export Downloads to" section.
At this time, iPod classic is not directly compatible with Amazon Music. Accessing iTunes to download purchased music, then syncing with your iPod would be the workaround. I can't provide direct steps for that, but hopefully another user may be able to assist. You could also reach out to Apple Support for more information on iTunes compatibility with your iPod.