I assume that you know all the advantages of having a rooted tablet, if not, a rooted one allows you to access a vast gallery of apps and games (especially the Android market) and enables you to install any app that requires access to the system files. Rooting also adds ability to modify the system files and even to replace them with other files. All these things posses the risk of getting phone damaged, so be careful while going through the processes as Make Tech Easier holds no responsibility if any damage happens to your device.
Pre-Requisites
Kindle Fire Root App (Download) Superuser (Download) Android SDK (Download)
Steps to follow to Root Kindle Fire on version 6.2.1 (Windows)
After obtaining all of the aforementioned files, install the Android SDK on your PC. Thereafter, install the Kindle Fire Root App on your tablet and then open it. It will prompt you with three options when you open it for the first time, choose the Root option from it. Now, extract the files from the Superuser ZIP archive to the ADB folder on your PC. Open the Command Prompt on your Windows using Win Key+R and then type the CMD in the dialog box that appears. CD to the ADB folder and then run the commands given below one by one.
After executing above commands, your Kindle Fire will now reboot. Once it is booted up, you will have access to the root. Enjoy!