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Try these steps please.
To delete a book, application or file directly from a Kindle Fire, it must already be installed on the Kindle Fire or Fire HD, not stored in the cloud. You can't delete books from the cloud using the Kindle Fire itself. Instead, you need the account management tools on your Amazon online account.
Log into your Amazon online account. Mouse over the top of the "Your Account" tab. Click "Manage Your Kindle" to access the management tools. The screen displays all of the books and applications that you have purchased from Amazon for your Kindle Fire.
Locate the book you want to delete in the list, and then click "Actions" beside the listing. Select "Delete From Library" in the Actions menu.
Click "Yes" when asked to confirm the deletion. Swipe your finger down from the top of any active screen on your Kindle Fire and choose "Sync" to synchronize the data on the Kindle Fire to the cloud and remove the deleted book from the cloud screen on the Kindle Fire.