***Programs Alive is not responsible for anything that go wrong while doing this.***
Before you continue, you will need to meet a few pre-requisites.
Firstly, your Kindle Fire must be rooted. Secondly, you must install
TWRP 2.0 – a touch-based custom recovery for the Kindle Fire. You can
follow our guide on how to root the Kindle Fire and check out
Liliputing’s guide for installing TWRP.
Step 1: Download Android 4.0.3 ICS Experimental Build [MediaFire]. Transfer it to the root of your Kindle Fire’s internal storage so you can flash it later.
Step 2: Shut down your Kindle Fire. Once it is
completely turned off, tap the power button to turn it on. When you see
the yellow triangle on the display, press and hold power button until
you boot into TWRP.
Step 3: Take a backup from the backups section on TWRP. This will come handy later on if you wish to revert back to your current state.
Step 4: Wipe out everything from TWRP i.e. data factory reset, wipe cache and wipe Dalvik cache.
Step 5: Tap Install and select the file you transferred to your Kindle Fire in Step 1. Once selected, tap flash.
Step 6: From the main menu, tap reboot system.
If you followed the steps correctly, your Kindle Fire will now boot
into an experimental build of Android 4.0.3 Ice Cream Sandwich based on
CyanogenMod 9.
For further queries, check out the official thread on XDA.