If and user has bought a book but is not able to download it on the Kindle Fire HD Device, then you have to find the root cause. Please check the payment method online if this may not be a reason. The payment method might not be valid or you might the information might have not completed. Go to “Manage Content and Devices” then “settings” and then “edit payment method” and do the required changes.
Another reason of your book or content not to be downloaded you might have filtered content over your home screen so that it won’t display all the titles. You should be going on the top of your screen over your Kindle and hot “By Most Recent First”. Now, you should be able to see the title of the most recent book purchased. You can also try to reset the Kindle Fire HD and see if that helps.
If you have done all of these things and still cannot download the books, then you can try and take help from Kindle Customer Support Phone Number by calling 1-866-400-1703