Step 4: When the convert window appears, make sure that the output format is set to "MOBI."
Step 5: Click on "MOBI Output" from the left column and delete the [PDOC] tag in the "Personal Doc tag" section.
Step 6: Click the OK button to start converting your e-books.
Step 7: Once Calibre has finished converting your e-books, copy your e-book files to the "Books" folder on your Kindle Fire. Remember, you'll need a micro-USB data cable (not included with the Kindle Fire) to transfer files to your Kindle Fire.
Step 8: Check the "Books" section to make sure your e-books are there.
That's it. To delete the PDOC tag permanently in Calibre, go to Preferences > Output Options > MOBI Output and remove the tag there.
A side benefit to converting your e-books in Calibre, is that it shrinks the size of the Mobipocket file (.mobi). Since the Kindle Fire doesn't have any memory expansion slots, converting your e-books may end up saving you a lot of storage space on your Fire.