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Your Kindle Fire *is* the Amazon app, essentially. You do not need an Amazon app, nor a Kindle Reader app, the Kindle device does that for you.
1. tap on the 'antenna' icon, and select your WiFi network, then connect to it - if you have not already.
2. Register the new Kindle with your Amazon.com account (if you haven't already.) This can usually be done by this process more or less: Settings - then Registration - then choose whether you already have an Amazon.com account or not - use the one you already have if you already have one - and register the device by entering your Amazon.com account username/email and the password ***** that Amazon.com account.
3. If bought from Amazon at very least, your books are always available in or from your Amazon.com account for re-downloading as needed. So, once registered on the new Kindle, you may download the books once again. If you have already bought some, you don't need to buy them again, in other words: your new Kindle may download copies of the books you have already bought in the Amazon.com account you have registered it to.
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