** THIS WORKED ON MY DEVICE BUT IT MAY NOT WORK ON YOURS. APPLY AT YOUR OWN RISK **
This has been tested with the unlocked US version running 4.6.1.
This procedure installs superSU root binaries and busybox on your system.
Make sure your PC can communicate with your fire phone via adb.
The success of this method depends on following the procedure very carefully. So read the instructions and make sure you understand every step before you try it.
1- Install and run Kingroot 4.0. You can google and download it or you can use the one in the attached zip file. When Kingroot runs it is all in Chinese, but basically you need to be connected to the internet for it to work. It will do its thing and show progress up to 100% after which you can exit the program. Now your phone is rooted. The following steps replaces the Kinguser with SuperSU.
2- Unzip the attached file in your adb directory and then open an adb terminal and make sure the PC can see your phone (you can check that by typing adb devices). Then type the following:
adb push su /data/local/tmp adb push busybox /data/local/tmp adb shell
mount -o remount,rw /system cat /data/local/tmp/su >/system/xbin/daemonsu && chmod 0755 /system/xbin/daemonsu cat /data/local/tmp/busybox >/system/xbin/busybox && chmod 0755 /system/xbin/busybox daemonsu -d &
5- At this point, leave the adb terminal window running and go to your phone, open the Kinguser app, open settings (the wheel at the top right corner of the screen), Root authorization setting, and Remove Root permission. The app will self-uninstall.
6- Uninstall the other two Kingroot programs that are still on your phone (KingRoot and the other one with the blue icon and Chinese text under it).
7- Back to the adb terminal, and type the following:
cat /data/local/tmp/su >/system/xbin/su && chmod 0755 /system/xbin/su busybox chattr -ia /system/xbin/ku.sud busybox chattr -ia /system/xbin/supolicy rm /system/xbin/ku.sud rm /system/xbin/supolicy rm /system/bin/rt.sh rm /system/bin/install-recovery.sh rm /system/bin/shipclean rm /system/bin/start-ssh busybox chattr -ia /system/etc/install-recovery.sh busybox chattr -ia /system/etc/install-recovery.sh-ku.bak rm /system/etc/install-recovery.sh rm /system/etc/install-recovery.sh-ku.bak rm /system/etc/install_recovery.sh rm /system/usr/icu/icusuflag.conf busybox chattr -ia /system/usr/iku/isu rm -rf /system/usr/iku rm /system/kroot_* rm /sdcard/kr-stock-conf rm -rf /sdcard/Kingroot rm -rf /data/data-lib/com.kingroot.RushRoot rm -rf /data/data-lib/com.kingroot.kinguser rm -rf /data/data-lib/king
8- Install superSU (from the attached file) on your phone, run it, and let it update the SU binary.
9- Reboot the phone. After about 5 minutes your root is ready.
Hint: It is a good idea to disable Amazon device client platform, DCP platform contracts, and two apps called System Updates in Amazon settings. They are responsible for regular updates, constant chatter with Amazon servers, and possible patching of your root exploit. Also disable Kinesis service which is responsible for major battery drain and heating. You will find it under settings, display, configure motion and gesture settings. Disable all.
1- Most of the problems that I noticed people have encountered is due to not reading the instructions fully. So make sure you read the OP word by word.
2- If you miss a step or mess up something go back to installing Kingroot and start over from the beginning.
3- If instant video or some other Amazon app doesn't work it is because you should run them at least once prior to rooting the phone.
4- Finally, I noticed that with an AT&T sim card in the phone Kingroot fails (why am I not surprised?) Either a reboot occurs in the middle of rooting or it completes the cycle without accomplishing root. If that occurs, my best advice is to change your phone company. If that fails, you may need to factory reset your phone or even install the firmware from scratch and try again without the sim card.