[Fire HD 6 and 7 General] bibikalka:
Update13, Oct 23, 2017: Everything still works with the latest 5.4.0.1, just grab the correct ROM file

Update12, Jul 23, 2016: Upgraded to FireOS 5.3.1, everything went smooth. It's not clear yet if 5.3.1 can be safely downgraded to 5.1.2 in order to get root. Stay put until we get some confirmation! It has been reported that the downgrade from 5.3.1 to 5.1.2 bricks the Fire HD!!! So downgrade to FireOS 4.5.3 instead, root, quickly turn off the WiFi, and then use this guide to go back to 5.3.1 (and do use 5.3.1 bootloaders!):

http://xdaforums.com/fire-hd/development/unbrick-fire-hd-6-7-flashing-lollipop-t3405797

Update11, Apr 29, 2016: I installed the new 5.1.2 build from Mar 30, 2016 via the instructions below (using TWRP), and everything worked fine. This version is not rootable by Kingroot (yet). One good option (if you have this version now) is to sideload via the stock recovery the rootable 5.1.2 from Feb 26 https://kindle-fire-updates.s3.amaz...HBV/update-kindle-20.5.4.2_user_542168620.bin , and then run Kingroot. See Update10 for other tips on what to do.

Update10, Apr 8, 2016: According to the reports, the stock 5.1.2 (Feb 26, 2016 build) is rootable via Kingroot (update to 5.1.2 via the standard Amazon procedures, try Kingroot several times). Block OTA updates (to prevent surprises): In Explorer go to /system/priv-app/DeviceSoftwareOTA and rename DeviceSoftwareOTA.apk to .apk_ . Then you can install GAPPS as per these instructions : http://xdaforums.com/showpost.php?p=65405511&postcount=268 Note that you will still benefit if you follow this guide: install TWRP, and reinstall 5.1.2 via the steps below and get all the Android goodies loaded at once (including Xposed) on an entirely clean /system partition with no Kingroot files.

Update9, Mar 21, 2016: The instructions below are updated for 5.1.2 . Kingroot does not work under 5.1.2, use adb sideload to 4.5.3 to get root! It seems that 5.1.2 has a bug where /sdcard is not visible for root (the issue seems to be this newer SuperSu version, not FireOS 5.1.2 ... I went back to SuperSu 2.46, and now it works as before). To be on the safe side, I modified scripts in post #2 to work with the newer SuperSu as well (but I don't recommend this newer SuperSu version ...) . According to a report, 5.1.1 bootloaders can be run after 5.1.2 without bricking. Regardless, here, all the bootloaders will be kept as 5.1.1 just to be sure

Update7, Feb 13, 2016: Instructions for the latest 5.4.1 update file (FireOS 5.1.1 -Bellini - with "blue shade") - Note that the instructions can be confusing, don't rush if you are not sure what you are doing (and especially if your Amazon warranty already expired) !!!

Update6: Since early Oct, there is a new evil (!!!) update named here as 5.2.2u2 (which bricked a few Fires), but thankfully the update glitches has been worked out!!! Back to business !!! Observe that once you booted 5.2.2u2 bootloaders (either through the Amazon update or the procedure below), there is no going back !!! The only other bootloaders you can run at this point are 4.5.3 as per post #2

Update4: Please do not deviate from the instructions, and do flash GAPPS during Step 1), together with Xposed. JMZ tool for installing GAPPS is not recommended!

For lazy ones I recommend skipping factory reset in Step 1) below if you already have Lollipop.

Install instructions.

Unless you have 4.5.3 bootloaders and TWRP at the moment, your path into TWRP goes via post #2 (and you do need TWRP to proceed!!!). No need to fear, I have made a simple script to flash 4.5.3 bootloaders and TWRP in just one click, see section "101" in post #2 !!!

Before proceeding, please write down your current FireOS version, and its date. To install the latest Lollipop you can pretty much start anywhere, these are rough suggestions how to get TWRP running in the quickest way possible :

unrooted Lollipop, pre-5.1.2 or 5.1.2, root via KingRoot (try several times), use post #2 for TWRP, re-load 5.1.2 from TWRP by following this post

unrooted Lollipop, alternative option, (note the version you have!!!), downgrade to 4.5.3 via stock recovery ADB sideload option (block updates immediately!!!), root 4.5.3, use post #2 to install TWRP

already rooted Lollipop, use post #2 to boot into TWRP, the bat script in section "101" is recommended (and can do a clean re-install of your current Lollipop version with the same procedure if you care)

rooted FireOS 4.5.x (latest Kingroot is known to root either 4.5.3 or 4.5.5.1, perhaps 4.5.4 & 4.5.5 as well) -then post #2 (if the bootloaders are not 4.5.3)

unrooted 4.5.x (>4.5.3 such as 4.5.4 or 4.5.5 but pre-4.5.5.1): disable OTA, run latest Kingroot, report back if failure, use post #2 for TWRP

unrooted whatever - write directly into memory 4.5.3 bootloaders & TWRP (somewhat slow, but can be an attractive option if you cannot root your version of Lollipop directly, and don't want to factory reset the device memore during the downgrade to 4.5.3 in order to root) :

http://xdaforums.com/fire-hd/development/unbrick-fire-hd-6-7-flashing-lollipop-t3405797

0) Before proceeding, ensure that you have a functional non-system launcher (install any as user app), or enable the stock Amazon launcher via adb if it's blocked (pm enable com.amazon.firelauncher) !!! Make sure it works. This will ensure that you can avoid problems later on when the /system partition is overwritten, and your non-Amazon launcher that was installed as a system app is gone. I had Nova as the system app (overwritten by the upgrade!), and Amazon launcher blocked, so after the upgrade to 5.1.2 there was no working launcher. Not good ... Had to do a couple of system resets and TWRP restores until I figured out what was happening ...

1) 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/customer/display.html?nodeId=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/SuperSU/UPDATE-SuperSU-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/showthread.php?t=3034811

(version xposed-vXX-sdk22-arm.zip )

flash Pico (Uni) GAPPS for 5.1 :

http://xdaforums.com/android/software/tk-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 (this is just to see if it works, for troubleshooting, but otherwise a meaningless step from the update perspective ...). Notice that at this point you no longer have TWRP. Since it does not boot with the 5.x bootloaders anyway, TWRP was replaced with the stock recovery that has some useful features, such as adb sideload. Later on it's possible to get back into TWRP from within the rooted Lollipop by following post #2.

3) reboot to Lollipop (takes ~15 minutes), and hopefully, it works.

Bricking warning !!! If you flashed the wrong bootloaders, and you get a black screen upon reboot, there is good news - you can UNBRICK !!! The bad news is that the procedure is quite involved, and may take quite a bit of effort. So measure twice, cut once !!! If unsure about bootloaders, ask here first before flashing, instead of coming back to complain about the brick later.

4) if step 3) fails, you get into working 5.2.0 recovery by pressing "Pwr & Vol+". At this point you sideload 4.5.3 stock, and go back to step 0). Come back here and ask questions (and thank me again for being able to recover so easily !!! :D )

5) make_space_v02.zip already disabled OTA updates , but please verify that you now have DeviceSoftwareOTA.apk_ block OTA updates (to prevent surprises): In Explorer go to /system/priv-app/DeviceSoftwareOTA and rename DeviceSoftwareOTA.apk to .apk_

6) Consider adding an option to switch from pure Amazon interface to almost pure Android and back on the fly:

http://xdaforums.com/fire-hd/general/fireos-4-5-x-root-quickly-switch-to-t3145613

Note: Using JMZ tool for installing GAPPS is not recommended, please flash GAPPS as per Step 1)

The next post discusses how to get into TWRP temporarily with Lollipop installed, and come back to Lollipop

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