rooting - How do I root my Kindle Fire?

There are a half-dozen or so questions on the Kindle Fire here where the answers involve having already rooted your device (including my recently-asked How can I get the Android Market installed on my Kindle Fire?). Ok, fine - doing dodgy stuff requires dodgy prep work. But... How?

I checked The Master List of Rooting Techniques, and found SuperOneClick suggested as the solution for the Fire... But as pleasant as this sounds, in practice this seemingly-easy-to-use tool proves inadequate: the device has been updated to break the technique it uses.

So what's the story (morning glory)? Am I stuck using the device the way it was intended to be used _^(shudder)? If not, what arcane magick will free me from these chains of conformity?

Answer

You can use Kindle Fire Utility to easily get root and Market with Google Apps.

It has support for the latest Kindle Fire firmware (6.2.1 currently).