You CAN root Amazon Kindle Fire HD
Gaining elevated privileges (popularly known as "root") is facilitated by an exploit found in Android 4.0 Ice Cream Sandwich that Amazon didn't fix before shipping the tablet. The fairly uncomplicated process gives the Kindle Fire HD a new trick up its sleeve -- using the Google Play Store, which provides access to all apps available there.
By making two software alterations, Kindle Fire HD 7 inch transforms from a standard Amazon device into a fully fledged Android tablet with Amazon software. It might not be the best of both worlds, but one thing is certain -- it's better than before. It's also one step closer towards an Android 4.1 Jelly Bean custom ROM.