XDA Senior Member prokennexusa wrote a root tutorial specifically for Mac and Linux users. It’s compatible with the Kindle Fire HD and the Kindle Fire 2. It’s been tested with Ubuntu and Mac OS X 10.5.8. It also requires 32-bit applications, so if you’re running 64-bit Linux you’ll need to get the IA32 libs or comparable package. On Mac, prokennexusa says you have to have x86. It won’t work otherwise.
The tutorial is admittedly written somewhat long. However, prokennexusa wrote it that way to help clarify the steps for those who are relatively new at rooting. It also includes some checks to make sure the process actually worked. So once everything is installed and ready to go, the whole process shouldn’t take more than 15-20 minutes. With this, practically all users can now root a Kindle Fire HD or Kindle Fire 2 easily.