If you are interested you can install Jelly Bean on your Kindle Fire, but keep in mind the release of the ROM is still in beta stage, therefore expect bug and issue. Thing that doesn't work reported is the codecs for HD video streaming are broken, therefore it takes Texas instruments update to run on the CPU of Kindle Fire. But the rest are reported to be working.
Step 1. Now download the Android 4.1 (Jelly Bean) ROM to be installed on your Kindle Fire from this link. Also Gapps, for you to flash your Kindle Fire tablet.
Step 2. Now you need to reboot your Kindle Fire into recovery mode.
Step 3. It is time to flash the Jelly Bean Rom and Gapps from ClockworkMod recovery, but be sure you to do a complete wipe of data also cache -- make sure you have firstly backed up as it will erase your entire data.
Step 4. After you boot up after flashing the ROM and Gapps do the following to fix Wi-Fi:
That's how to install Android 4.1 (Jelly Bean) on Kindel Fire, does it work for you?