To get a Leanpub book onto your Kindle or into your Kindle app, please follow the instructions below, which are also on your Kindle Settings page.
Note that this only works if the Leanpub book has a MOBI version. Most Leanpub books have a MOBI version.
[On a side note: here are some instructions for adding PDF files to Kindle: https://www.pcworld.com/article/2044412/convert-a-pdf-for-kindle-viewing-no-software-required.html]
The Easiest Way to Get a Leanpub Book Into Your Kindle App
The easiest way to get a Leanpub book available in the .mobi format onto any device is to open the receipt email for your purchase on your device, and then just click on the link for the .mobi version of the book in the email. You can also do this by clicking on the link for the .mobi version if you sign in to Leanpub on your device and select the book in your Leanpub library.
Other Ways To Get a Leanpub Book Into Your Kindle App
There are a few other ways to do this, including Leanpub's Send to Kindle link, Amazon's Send to Kindle app, and transferring the file via USB from your computer to your device.
First, Get Amazon to Allow Leanpub to Put Books onto Your Kindle
First, go to Amazon and let them know that it's okay for us to send things to your Kindle. Personal Documents Settings on Amazon and add email@example.com as an approved email address. (Look for "Add a new approved e-mail address" near the bottom of the page).
Every Kindle has an email address. You can find yours by going to your Personal Documents Settings on Amazon. It will be something like "firstname.lastname@example.org" or "email@example.com". Enter the "you_123" part in the form above and click the Save Kindle Settings button.
Second, Go to Your Leanpub Library and either Send to Kindle or Download
Once you're set up, go to your Leanpub library, select the book, and click the "Send to Kindle" link you will find there. (If you don't see the "Send to Kindle" link, that means this book is not available in the MOBI format required by Kindle.)
Alternatively, you can download the MOBI file for the book onto your computer or device and use one of Amazon's apps to get a book onto your Kindle.
Third, Go to the Docs (not Books) Section on Your Kindle
[UPDATE October 28, 2019: A customer has informed us his books showed up in the "Downloaded" space in Kindle, and he didn't have to go to a separate "Docs" or "Documents" section, so this part of our guide may (we hope!) be outdated.]
To read your Leanpub book on your Kindle, you will have to go to the "Docs" section underneath All Items in the main Kindle menu. Send to Kindle puts our books in "Docs", instead of the "Books" section. Presumably, Amazon must only think something is a book if they sell it!
A Note About File Sizes
The "Send to Kindle" feature on the Leanpub website only works for books whose MOBI versions are under 49 MB in size. If the book is over 49 MB in size, we won't show you any Send to Kindle links for it on the Leanpub website or in Leanpub emails, since they won't work.
Download the Book and Open It in the Kindle App on Your Device
Alternatively, if you have the Kindle app installed on a device, once you have downloaded the .mobi file from Leanpub, then if you double-click the file, it should open in the Kindle app.
Adding a Book to Kindle via USB
If you download the .mobi file to your computer, you can then connect your Kindle (or another device, like an Android device with the Kindle app) to your computer via USB, and then manually copy or drag the .mobi file for the book from your computer onto your device.
To learn how to get a file larger than 50 MB into the Kindle app on your iPhone or iPad, please read this blog post.