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You need to register the new iPad with your Amazon account. If you already registered it, then lets delete that app and redownload it. On your new iPad, tap and hold down the Kindle app and it will start wiggling. Tap the x icon to delete it. Then open App Store app and download the Kindle app.
Open Kindle and register/login with your Amazon account. This will re-register it. Now check under Cloud section and you will find the book there. If not, then you have to manually deliver the book to your new iPad from your computer.
On your computer or iPad Safari browser, follow the steps below
Please let me know if that didn't work, so we can continue troubleshooting.