Developer JMZ is on a roll! Not only did he manage to get the bootloader unlocked for both the Kindle Fire HD 6 and 7 he has also managed to get TWRP custom recovery ported over to both devices. With Twrp you will be able to fully backup your device, as well as install custom roms giving you the full AOSP experience. You can also flash various mods and add the Google Play Store to your device. Of course TWRP is a fully touch enabled recovery which is great for a device like the Kindle Fire HD! Once you have installed twrp boot into the recovery, choose the reboot system option, then chose to install supersu if you want to root your device.
via XDA