To get free ebooks, Amazon Prime members must access the Kindle Store using a Kindle e-reader, Fire tablet, Fire phone or computer. In the Kindle Store, Prime members have access to the Kindle Owners’ Lending Library. All eligible book titles display the Amazon Prime badge and show a Borrow...Where are my books?
Wait for a few seconds and then scroll down till you locate Books. Tap on Books/iBooks and make sure that the ‘Documents and Data’ row shows actual storage usage. This section indicates if your Books content was successfully downloaded to your iDevice.