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It should work on any device that has a Kindle app. You can see a full list of them on Amazon's Free Reading Apps page. Amazon supports a wide range of devices, it's one of the reasons why I use them as my ebook store. You can also use the Kindle Cloud reader if you want to read in your browser.
Now if only they would make it like that for Amazon Prime Video. I've never understood why Amazon makes it so their video service that is supposed to compete with Netflix can't be used with normal Android tablets and smartphones. It's a strange decision, and I suspect it will lead to a lot of people assuming that Kindle Unlimited will be unavailable as well.