Here's a good article we found about adding a PDF to Kindle:
But that's a bit complicated!
If you have an iPhone and you have the Kindle app installed, there's a much easier way.
Step One: On your iPhone, open your email app.
Step Two: Find the purchase email you received from Leanpub.
Step Three: Click the PDF download link in the purchase email from Leanpub.
Step Four: Choose the "Open in..." option at the bottom right.
Step Five: Select "Kindle" from the displayed options; you may need to swipe left a bit to find it.
Step Six: Go through the Send to Kindle process; you'll have to add an "Author" name yourself, sorry about that!
Step Five: Choose "No" when it asks if you want to convert the file to Kindle format (assuming you really do specifically want the PDF!)
Step Six: Voila! The PDF will appear in the Kindle app on your phone, and it will also magically appear in your Library on your Kindle reader, after you give it a few minutes to sync.