Wish it would also sync the non-Amazon books, though. Maybe I am not proficient enough yet, but so far I had to copy ebooks into obscure directories by hand (especially interesting on the Android Kindle reader).
Just add your email to "Approved Personal Document E-mail List" under your kindle settings https://www.amazon.com/gp/digital/fiona/manage/ref=ya_14#pdo...
Then you can sync all your books through mail.
Set up a Tasker-profile to automate the copy-process of all epub/mobi/whateverfileextension to the folder of your choice on your Android.
Or setup a spideroak sync folder for the ebook-folder on your android, and just sync your non-amazon books through spideroak.
I have never gotten anything except Amazon purchases to sync to my Android Kindle app. I can manually copy .mobi (and I think .azw) files to my Android and the Kindle app will read them, but there's no Whispersync between devices except for official Amazon purchases. It's the same with my iPod Touch but not many people realize you can manually copy books to the Kindle app.