Trying to install update-kindle-prerooted.6.3.3.v1.zip (coming from 6.3.2 rooted): I had TWRP 126.96.36.199 and got stuck on "Doing Some Stuff". I loaded TWRP 188.8.131.52 and got stuck at the same place. I installed "zip-Cannibal-Open-Touch-Recovery-2.1.zip" instead and with that recovery I was able to get 6.3.3 installed. It's sitting on the animated "kindle fire" logo right now for a while (which I expect because of wiping both cache and davlik cache).
Update: First boot finished. That took 4 or 5 minutes. (no biggie)