I've installed FireFireFire and TWRP on my Kindle Fire. That went ok and I can boot into TWRP. Then I tried installing many custom ROMs (SimpleCM9, jandycane, MIUI, AlienDroidV4.0.zip) but all with the some result - flash ok, reboot, boot logo/animation of custom ROM, then reboot and Kindle hangs on next boot.
TWRP 2.2.2.1