In general, if you have a subscription through a third party like Amazon you'll only be able to use that subscription on their devices. The same thing is often the case with subscriptions through Roku (i.e., you can't use them on Amazon devices). There are exceptions. If you can log in on the Starz site using your Amazon email address then you should be able to use those same credentials on other devices. Often you need to establish a password on the provider's site, so you may have to use the "forgot password" option assuming it even recognizes your Amazon email address. Once you have an email address or username and a password you should be able to use those on the Roku Starz channel/app (not Starz through The Roku Channel).
https://channelstore.roku.com/details/14b058d40b5893ab8b3883e4ed2f2815/starz
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