Titanium Backup is the primary reason that I want to root Amazon Kindle Fire. Titanium Backup needs root access to backup / restore apps. So how to root Kindle Fire? Very simple, just use SuperOneClick to root Kindle Fire. Really, just one single click.

Root Amazon Kindle Fire with SuperOneClick
Prerequisites
Okay, here is the catch. You need to have Kindle Fire adb USB driver installed first. SuperOneClick v2.3.2 has auto USB driver installation function but I did not try it since I already setup Android SDK Development Environment and Kindle Fire adb USB driver myself. And I prefer this way because they are needed to install CM7 ROM too. How to setup? Follow this guide ~ How to install & setup Android SDK Development Environment? And How to install Kindle Fire adb USB driver?
How to root Kindle Fire?
Congrats. You can start using Android applications that require root access from now on like example below.

Titanium Backup on Kindle Fire
Download SuperOneClick v2.3.2 here.
Tags: Amazon, Kindle Fire, root, SuperOneClick
everyone who cant root read this: it will not root because of 6.2.1 update. you must root it a different way. Go to http://www.redmondpie.com/root-kindle-fire-6.2.1-using-burritoroot-how-to-tutorial/ . this works do it
I finally get the ADB working, now the SuperOneClick freeze during the process. What can I do?
Which Kindle Fire software version are you using?
6.2.1
SuperOneClick won’t work on 6.2.1. Try this instead – http://www.jayceooi.com/2011/12/29/how-to-root-kindle-fire-with-burritoroot-video/
Hi Jayce
Does superoneclick v2.3.3 work on Kindle Fire 6.3?
I cannot go through rooting by using superoneclick v2.3.3. Is that because I have rooted my kindle fire by using Kindle Fire Utility 0.9.5?
many thanks,
No, it does not support 6.3.
What tools can I use to root Kindle Fire 6.3?
Is Kindle Fire Utility 0.9.5 working?
thanks,
Kindle Fire Utility v0.9.5.
It should but I did not try it personally.