There are a few things to try if you're having trouble deleting books from your Kindle app on iPhone:
-First, make sure that you're signed in to the correct Amazon account. You can do this by tapping the Menu icon in the top-right corner of the app, and then tapping Account.
-If you're still having trouble, try restarting your iPhone and then deleting the book from the app again.
-If you're still having difficulty, you may need to contact Amazon customer support for help.