The hacker is going by the name JackpotClavin, and he's successfully compile a version of CyanogenMod 7 so it runs on the Kindle Fire. I've mentioned CM7 before; it's a popular custom firmware for Android. You can run it on the Nook Color and a lot of other tablets.
This version is by no means ready for the end user, and it doesn't even sound all that stable. According to JackpotClavin, there's still a few problems that need to be fixed. He has Wifi working (but it won't connect to any network). The new KF also charges. And what's even better is that it looks like the KF can be unrooted after the fact, returning it to its original Amazon clunkyness.
He also said that he plans to post instructions and a ZIP file with the needed components later this week. It's only been 2 weeks since the Kindle Fire shipped, so this excellent progress.
You can find out more over at XDA Forums.