Although most of the hardware functions are working right now, Audio is still an issue. So, if you need audio as part of your daily usage, CM7 is not ready for your Kindle Fire. Due to the absence of physical keys from the tablet, installation is a bit tricky and JackpotClavin has given a modified version of CWM recovery to help you in flashing the firmware.
I would suggest the not so adventurous users to wait for a while until a more polished version is available.
Check out more on installation and download at the original thread.
