Long time reader, first time poster. I wasn't able to find any confirmed reports on whether or not this method still works with system version 8.3.1, even though the other Windows script has some conflicting reports on success. I felt adventurous, so I tried it and it did work! Here are a couple of notes:
1. The download links seem to be working fine. I think one of the Dropbox links didn't work for me, but the attached files list at the end of the orginal post seem to be mirrored elsewhere and they work.
2. I'm still on Snow Leopard (Mac OS X 10.6.8), so I found that I couldn't install the latest JDK from Oracle (installer says you need 10.7) and I couldn't download older versions without an Oracle Developer account. Instead, I followed the top answer from this thread
to override the requirement. Briefly, you install Pacifist and use it to run the installer (for the latest JDK). Afterwards, you may have to go to System Preferences to change your Java settings to use the new JDK by default.
3. The su invocation did not work for me. I used 'sudo' for each command.
4. With the JDK in place, the rooting script worked flawlessly!
5. I had a slight issue disabling OTA, which I wrote about in that thread
6. I also had an issue installing the Google Play Store, which can be found (along with my solution) in it's own thread
It's now been over a week and my KFHD is running better than ever! I do notice some kinks every once in a while, like the Amazon Appstore had trouble loading once and the default Email app can't fetch emails sometimes, but nothing so far that hasn't resolved itself with a simple reboot. Thanks for the instructions and everyone's input!
Kindle Fire HD 8.9"
System Version: 8.3.1_user_3150820