If you're on the most recent software, you don't need the sdk to root. All you need is the Kindle Fire Utility from XDA (KFU). From there, I would recommend making sure you have the most updated driver possible, so when you plug in your kindle, it should say "android phone--> adb composite interface"....from there you need to download the FFF 1.4a bootloader (also on xda) and transfer it over to your Kindle's SD card. Then you want to install TWRP, boot into recovery, then flash the FFF bootloader. There is no point in running burrito root or any of the other roots unless you really want a rooted stock rom. And I can't imagine why you would just install a custom rom if you're going through all this trouble. Installing TWRP and the FFF bootloader will enable you to flash custom roms to your heart's content. Hit me up if you need further instructions. Read, read and read some more is the best advice I can give you.