I think, recently, Amazon has been including a few free/public domain books automatically when you get the app for Android. . . . .it is possible that if you delete that from your Android device, it might be gone forever. And it's possible it's NOT available for other Kindle devices that may be registered to the same account.
Otherwise, Lin is absolutely correct: you buy it once, you can use it on any device. Amazon keeps a copy available for you in your archive and you can get it back any time. Even while it's on one device, you can download it and read it on another device on the same account -- up to 6 (usually) devices at a time. It's a great way to share books among family members or within a small group of friends.
