Before you follow that thread, which is intense, try to reboot to recovery on your current OS. Use the adb reboot recovery command, and you should see the sideload through ADB option. I did. I then flashed 4.5.3, rebooted to setup (no wifi). Then, from adb in your laptop, adb install Kingroot and the JMZ Tools so that you can disable OTA. Disable OTA (pm block com.amazon.otaverifier), and let Kingroot install root with wifi enabled. Once root works, adb install Flashify to install the twrp image that you will copy to the device. Reboot to recovery, and flash supersu.zip.
Follow the steps from this thread:
https://xdaforums.com/fire-hd/general/how-to-upgrade-to-lollipop-root-gapps-t3163950
boot into TWRP, and, in a single session (!!!!!)
(Optional) clear cache/dalvik (to shrink the backup size), run TWRP backup to a USB drive via USBOTG cable for your /data partition
(Optional) do factory reset (can skip if you already have Lollipop),
flash the latest FireOS from this official Amazon link (rename *bin to *zip such that TWRP can recognize it):
https://www.amazon.com/gp/help/custo...deId=201596850
If for some reason you need a different FireOS version, grab the file you need from the links in this post.
flash 5.2.0_stock_recovery_only.zip below. If you kept track of your prior FireOS versions and know what you are doing, you can flash
5.4.1_1133_stock_recovery_uboot.zip from post #2 (this will flash 5.2.0 stock recovery & 5.4.1 bootloaders). Note that if you downgraded from FireOS 5.3.1 to 4.5.3 to root, you must flash 5.5.2_1534_stock_recovery_uboot.zip instead, this will put the required 5.3.1 bootloaders back.
flash the attached make_space_v02.zip (this will remove moffice and weather to make room in /system for GAPPS , can always install this stuff from Play Store)
flash Supersu.zip
https://download.chainfire.eu/696/Su...erSU-v2.46.zip
flash Xposed for Lollipop 5.1 (if you want it for misc modules, highly recommended to do this just in case)
http://xdaforums.com/show....php?t=3034811
(version xposed-vXX-sdk22-arm.zip )
flash Pico (Uni) GAPPS for 5.1 :
http://xdaforums.com/andr...gapps-t3116347
clear cache/dalvik in TWRP
Another reminder: If you are absolutely sure that you have never run FireOS 4.5.5.1 bootloaders or Lollipop with anything but 5.2.0 bootloaders, you can flash 5.2.0_stock_recovery_uboot.zip from post #2 here, this way you preserve the well behaved 5.2.0 bootloaders. If you are not sure about any of this, don't do it !!!
2) reboot to recovery, you should see stock 5.2.0 recovery