If your friend sent you some books that he got from
Amazon (that can be read with the Kindle app), you can't read them.
Amazon, like most other e-book stores, have software on each e-book to protect from unauthorized copying and sharing of books. This software is Digital Rights Management (DRM) and it makes it so that a book can only be read by the purchaser.
Due to this DRM, your friend cannot share electronic books with you. You'll have to purchase your own. Sorry.
By the way, this has nothing to do with Dropbox, which is "merely" an online cloud storage.
Marilyn