Folks who have updated their Kindle Fire to Android 6.2.1 and want to root it they can follow the guide below which will help them to do so through Kindle Fire Utility.
Root Kindle Fire 6.2.1
Download Kindle Fire Utility and extract it
Connect your Kindle Fire system through USB
Tap on “Disconnect” button which will appear on your Kindle Fire screen
Navigate to extracted Kindle Fire Utility folder and double click on “install_drivers.bat” file to install drivers
Double click on “run.bat” file inside Kindle Fire Utility folder
When Kindle Fire Utility window will appear, press “3″ from keyboard to select the option “Install Permanent Root with Superuser” and hit “Enter” key
Rooting process will start, so let it finish
Your Kindle Fire will get reboot
Just, disconnect Kindle Fire from system and that’s it
Enjoy, your Kindle Fire on Android 6.2.1 is rooted now.