For those of you with Mac OSX or Linux, you can root it using this method:
Step 1. Go to Settings->More->Device and make sure “Allow Installation of Applications” is checked “ON”.
Step 2. Connect your Kindle Fire to your computer via micro-USB cable. And hit “Disconnect” to turn off the USB disk drive mode.
Step 3. Download KindleFireRootMacLinux.zip and unzip to the root directory of your hard disk such as c:\KindleFireRoot.
Step 4. Open up a terminal.
Step 5. Browse to the KindleFireRootMacLinux directory by typing:
Step 6. Type:
cp adb_usb.ini ~/.android/.
*Note – You might have to add “sudo” for Ubuntu
Step 7. Type:
If you get a bunch of numbers and letters, that means you are good to go.
Step 8. Type:
Step 9. Your Kindle Fire should do its rooting and reboot.
You can verify you have SuperUser app by going to Settings->More->Applications->All Applications.