I have a first Generation Kindle Fire. I rooted it when I first got it Christmas 2011, but with each upgrade it gets unrooted. I just found and tried out this great tutorial on rooting your KF using a Mac. Most tutorials are for the PC. This tutorial is specifically for the 1st Gen KF with the 6.3 or 6.3.1 OS.
To use the Kindle Fire Utility Software on my Mac I had to enable execution of “Applications downloaded from Anywhere” in the Security Settings.
Great Tutorial for Rooting your 1st Gen Kindle Fire on a Mac is here