The Kindle Fire is rootable via SuperOneClick.
Getting ADB Working (Windows)
1. Make sure you have JDK7 installed.
2. Install the Android SDK 
3. In the SDK Manager, Uncheck Android 4.0, Check Android 2.3.3, and check the Google USB Driver Package (under extras). Install them.
4. Paste the following code below [Google.NTx86] and [Google.NTamd64] located at C:\Program Files\Android\android-sdk\extra\google\usb_driver\android_winusb.inf
%SingleAdbInterface% = USB_Install, USB\VID_1949&PID_0006
%CompositeAdbInterface% = USB_Install, USB\VID_1949&PID_0006&MI_01
5. Navigate to your home directory (C:\Users\username\), inside the .android folder, create/edit a file called adb_usb.ini. Make sure the contents of the file is nothing but 0x1949.
6. Plug your kindle in with a micro-usb cable, and go to device manager. Right click your unknown device kindle, and click "Update device software", and click Browse my computer. For the file location, it's C:\Program Files\Android\android-sdk\extra\google\usb_driver.
7. Open a command prompt and cd to where you have the sdk installed, and then cd to platform-tools.
8. Upon typing adb kill-server, followed by adb devices, you should see a device in the list (otherwise you did something wrong!)
1. Download and extract SuperOneClick. 
2. Run SuperOneClick and click "root".
You've rooted your kindle! What's next?
Google Market Install: 
Unofficial CM7 Install: