Rmove a document from Kindle Library on my iPhone

I don't have the Kindle app on my iPhone but do on my iPad so the following may be slightly different than what you see on the iPhone. On the iPad, open the Kindle app and go to the Library (if in a book there is an icon with 3 horizontal bars and Library is one of the choices when you tap the 3 bars icon). Once in the Library, press and hold the icon of the book you want to delete and one of the choices will be "Remove from Device."

http://www.amazon.com/gp/help/customer/display.html?nodeId=200298460