Those of you interested in rooting your Fire TV Stick will be happy to learn that the new revised 126.96.36.199 software update, that recently started rolling out, is still rootable using the Kingo Root app. I have verified this myself. If your Fire TV Stick is running software version 188.8.131.52, and you want to root, you should allow it to update to 184.108.40.206 and then block updates. One of my Fire TV Sticks running 220.127.116.11 would not root with Kingo Root, but after allowing it to update to 18.104.22.168, I was able to successfully root it on the first try using Kingo Root.
It’s recommended that you wait for custom recovery and a pre-rooted ROM for the Fire TV Stick to be released before you root the device. However, if you can’t confidently block updates externally, then you should root with Kingo Root and block updates internally. Rbox still plans to release TWRP custom recovery and pre-rooted ROMs for the Fire TV Stick, but it is unknown when that will happen. Kingo Root is not able to root the 1st or 2nd generation Fire TV, regardless of which software version is installed, so there is still no way to root a Fire TV running 22.214.171.124.