If you don’t want to use Amazon’s Music Unlimited service anymore, canceling it is a pretty straightforward process. It only takes a minute or two and there are multiple ways of doing it, depending on where you signed up for it.
However, you can’t end your subscription through the Amazon Music app itself, which is a bit strange. So to get the job done, you’ll have to use a web browser or go through the Apple App Store if you purchased a subscription that way.