One of the modders over at XDA, JackpotClavin, was able to get CyanogenMod 7 up and running on his rooted Amazon Kindle Fire. It's still in the early stages and is running fairly rough according to his feedback. Here's a quote from theVerge article,
How many of you guys want to get this tablet just to play around with modding it?Wi-Fi is operational, but the tablet's touchscreen controller is interpreting input incorrectly, which is rather slowing down testing on what else might or might not work.
Source: Kindle-FireForum via TheVerge and XDA