Unable to download a book from amazon to ipad mini

Did you set up the Kindle App with your Amazon account, and add the iPad to the devices on the account (amazon web site)?

You also may want to be a little more specifc about what "can't download" actually means.

Ordinarily, you would buy the book through Amazon's web page, then login to your account from the Kindle app and sync the reader. That should then download your purchased books into the Kindle app's library on the iPad.

You do need to register your iPad with Amazon under the "manage your account section" so it knows it is linked to your account and is one of your authorized devices to download from your purchase history.