It is easy to play LibriVox free audio books on your iPhone.

LibriVox is a non-profit organization that provides free downloads of audiobook versions of works in the public domain.  They are always recruiting volunteer readers to record more books and quality review audiobooks about to be released.

Here's how you can download and play audiobooks from LibriVox on your iPhone (iOS version 12.1.4):

1. On the iPhone, use the Safari browser (its icon is in the dock at the bottom and looks like a compass) to go to LibriVox.org.
2. Find a book you want to download.
3. Tap Download.
4. Tap Files. (If Files is not an option, tap More, then tap Save to Files.)
5. Tap Pages.  (If Pages is not visible, tap On My iPhone to disclose it.)
6. Tap Add.
7. Open the Files app by tapping its icon.
8. Tap Browse.
9. Tap On My iPhone.
10. Tap Pages. 
11. Tap Preview Content.
12. Tap the play button.

• To jump ahead or back on the track playing, tap and hold the sound waves above the play/pause button and drag.
• To navigate various chapters, tap the icon of a bulleted list.
• To leave, tap the file name at the top, then tap Done.

To delete a ZIP file (not individual chapter files), navigate to Files > On My iPhone > Pages, and swipe the ZIP filename to the left, then tap Delete.

Notes:

Even though multiple chapters are downloaded as a single ZIP file, the Preview Content option in Files will play them as described here.

All of this is done over wi-fi without the use of iTunes or a computer.

If you don’t like using the iPhone to navigate the LibriVox site, you can use a computer and any browser to go to the site and download the files to the computer.  Then: 

1. Log into your iCloud account and upload the file(s) to iCloud Drive.
2. On the iPhone, open the Files app.
3. Tap Browse.
4. Tap iCloud Drive.
5. Navigate to the folder and filename you saved.
6. Tap the download icon.
7. Tap the Share icon (a little box with an up arrow).
8. Tap Save to Files.  Resume with step 5 in the first set of steps above.

These same instructions will work with an iPad, although the location of the controls on the screen may differ from where they are on an iPhone.