To remove the book, go to the Kindle app home page, select the book desired and swipe from right to left. A red archive button will appear, tap it and the book is removed from the app. To download it again, go to cloud view and tap the down facing arrow that is located where the archive button was.
To deregister the Kindle app, tap the settings icon on the bottom right of the Kindle home page, tap registration, then tap deregister this Kindle. To re-register the Kindle, go into the settings like you did to deregister it, the button will now sat register this Kindle, tap it and follow the directions to re-register your Kindle app.

I'm glad it worked out for you. Thanks for the feedback, it's nice when we know our advice worked.