1. Factory reset your WHOLE device before flashing this.
2. Convert your bin file into a zip and name it update.zip (go into properties and make sure your well known file extensions aren't hidden)
3a. Go into old TWRP (don't flash 126.96.36.199 just yet)
3b. Wipe Data, Cache, and Dalvik Cache. DO NOT wipe system.
4. Flash the update.zip. You shouldn't have any problems with flashing it and it should boot up when you restart it. (if you have troubles flashing it, go into ubuntu and change the update-script in the first few lines (codename) from "blaze" to "otter". Save it. Now put it into your SD card and flash it and NOW it should work.)
5. Go into Kindle Fire Utility (found here), run "run" and install FFF 1.4a (make sure you have drivers installed before doing this, duh )
6. Press Shift and Right click the "tools" folder in the KFU folder and click on "Open command window here"
7. Download TWRP 188.8.131.52 found here (select otter 184.108.40.206)
8. Restart your kindle fire and type in "fastboot flash recovery twrp.img" (rename it twrp.img or it won't detect it but move it inside the "tools" folde" so it'll find it). When your kindle starts up, it will detect it and flash the image.
9. Congratulations, you have successfully installed TWRP 220.127.116.11 without data mounting problems anymore. (this is what I followed to fix my problem.)
10. Flash CM11 and Enjoy
Also, if you want to dualboot, just use this and follow the guide..
FuZZ_+Hashcode for CM11
awidawad for KFU
Dees_Troy for TWRP
Amazon for the firmware
Me for discovering this
Please click thanks this guide helped/inspired you.
Hope it helped anyone who had the same problem