I am doing this with I have Itunes version 12.2.1.16.
1. Download the Mobi File to your computer. For example, Smashwords.com has lots of free ebooks.
2. Connect your phone to computer and run iTunes.
3. In iTunes, click on the iPhone icon (top left).
4. Click on Apps (middle left). The scroll all the way down. The Kindle app should be listed under file sharing.
5. Click on the Kindle Icon.
6. Drag and drop the mobi file to the right of the Kindle icon in the documents section.
7. Click on sync (bottom right).