There is even an easier option. In Dropbox, when you click "export" there is a button on Android that sais "send to kindle". You can then choose to which devices it should be synchronized, and the stuff gets uploaded somewhere. You have to choose "Synchronize" once to really see the books then, but you are done.
This looks like Amazon allows to do this and has even implemented it.
Surprisingly not dongled down to insanity, chapeau, Jeff Bezos