CyanogenMod (android) on Amazon Fire Phone Tutorial
Links
KingRoot
http://androidxda.com/download-kingroot-application
SafeStrap
http://forum.xda-developers.com/fire-phone/development/recovery-safestrap-v4-0-1-t3149888
Amazon Fire Rom (optional) (read the description please)
http://forum.xda-developers.com/fire-phone/development/safestrap-v4-flashable-stock-image-t3150531
CM11 & GAPPS
http://forum.xda-developers.com/fire-phone/development/rom-cm-11-20150706-unofficial-t3151443
SuperUser (also optional. this just manages root permission for apps that use it)
http://forum.xda-developers.com/showthread.php?t=1538053

After you are done there is no camera so go to Google Play Store and download Open Camera or another camera.
or click on the link below
https://play.google.com/store/apps/details?id=net.sourceforge.opencamera&hl=en

Note: My phone’s firmware was 4.6.1. And I know there are some misspelling this is because I rushed this video and its my first edited video.

Another Note: I transfer the files on the download folder of my phone, but you can transfer them anywhere as long as you know where they are. The quality on youtube gets cut off so it is not that clear.

Also if you guys have time, thank the developers in xda.

Thank You For Watching.

Edit sep. 11, 2015: There is another rom called Slimkat which can be found below. The installation is the same except the Rom is different.
http://forum.xda-developers.com/fire-phone/development/rom-slimkat-safestrap-v4-2015-08-28-t3188787