Video demonstration: installing Jelly Bean for the Kindle Fire!
How & What You Need:
Jelly Bean for the Kindle Fire: This process is completed online using the Goo Manager app (from the Play Store) and does not require any special software – or even a computer! It is all done on a ROOTED Kindle Fire. If you have not yet rooted your KF, then visit our guide here.
Here is a video of it in action:
Install a CUSTOM ROM (Including Jelly Bean)
This is a short course on how to add/flash a custom ROM to your ROOTED Kindle Fire. If you have not yet rooted it, then follow our guide here: http://raywaldo.com/2012/01/kindle-fire-works-great/
You can use the Goo Manager app (available on the Play Store) to install TWRP, download the ROM & Gapps zip files, back up the existing system, wipe / restore to factory, & flash the downloaded zips. (To install TWRP with Goo, just select the “Flash ROM” option and it will step you through the process.)
From Goo Manager:
- Browse compatible ROMs
- Drill down to a particular ROM (select from any of the lists since they are all “compatible”)
- Download the ROM file
- Be patient (watch the download in the notifications)
- Follow the on screen directions
Alternately, just Download ROM & GApps for JB. Then, boot into TWRP and complete the following process (same for any compatible ROM): Here is the link to the XDA thread for one of the best Jelly Bean ROMs available for the Kindle Fire (first gen): [JB 4.2.2] CM10.1/SGT7 for the Kindle Fire 
- Backup your existing system
- Wipe cache & dalvik
- Suggested: Reset to Factory
- Flash the zip for the custom ROM
- Flash the zip with the GApps
- Reboot & enjoy!