Amazon's recent root-destroying Kindle Fire update 6.2.1 not only removed existing roots but disabled the easiest means of re-rooting—SuperOneClick. But what if you want to keep your root more than update? Gizmodo's Chris Beidelman has devised this ingenious and simple workaround:
Kindle Fire 6.2.1 breaks root and you cannot re-root. To prevent this, simply install DroidWall. If you are afraid of downloading the update and want to keep wifi disabled, just do a google search for Droidwall.apk and sideload.
Once installed, launch Droidwall. Make sure the mode says "Mode: White list (allow selected). You will have to manually select which apps to give Wifi access to (I selected Email, Browser, Netflix, and Amazon Video on Demand). You should only select the apps you REALLY want to give access to. Then hit Menu and Apply Rules. Enable Wi-fi, and you should be good.
I tested while running Wireshark and watched the bandwidth according to my Tomato router - no more huge files being downloaded.
Granted, there are other methods for sidestepping the auto-updates but they are much more involved and have a spotty success rate. If you have success with this method, let us know in the comments!