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All you have to do is, download the Kindle application on your iPad from App Store and login to your Amazon account on your iPad and you will find all the books you've purchased under Cloud or Archived section.
On your iPad, open App Store. Search Kindle and download it. Tap the Get or Cloud button to download it.
After downloading, open Kindle app. Login with the same Amazon account you used on your Kindle (this is important). You will find the books under Cloud or Archived section. If you don't see them, then you can deliver the books to your iPad from Amazon website. Follow the steps below
Please let me know if that didn't work so I will continue to help you.