Tap the Cloud tab at the top. It's at the top of the screen, next to "Device". This will display the audiobooks that you own but have not downloaded to your iPhone or iPad. Tap the image of a book with a "download" arrow on it. If you see the download icon in the lower-right corner of a book's cover image, that means the book can be downloaded.What apps have free audio books?
LibriVox is a volunteer-powered service that offers free audiobook versions of classic books that entered the public domain in the US. LibriVox Audio Books Free is an Android app that’s developed by a different company (Book Design). Nevertheless, it offers free audiobooks from LibriVox as well.