[Fire HD 8 and HD 10 Original Android Development] deverro:
Yesterday i managed to root updated FireOS and install Lineage 12.1, so, here's my story :D

Version 5.6.6.0 build 654620620,

on Linux KDE Neon.

Installed python3, PySerial, adb, fastboot dos2unix as described in this and other posts.

sudo apt update
sudo add-apt-repository universe
sudo apt install python3 python3-serial adb fastboot dos2unix

Downloaded the following attachments from the first post : amonet-douglas-v1.2.zip and brick-douglas.zip

Extract both files to the same folder

Enable Developer options and enable ADB (inside debugging options) on Amazon tablet

Plug in the tablet (has to be turned on)

Now comes the commands execution part. So, open the terminal in Linux (lines that start with // are comments and should not be run from command line - if you copy paste)

sudo systemctl stop ModemManager && sudo systemctl disable ModemManager

adb devices
// there should be an item listed
// to be sure, you can unplug and run it again, if it's empty,
// ou know tablet can connect, so plug in the tablet back

adb reboot bootloader
// reboots the tablet and awaits commands

sudo ./brick.sh
// type YES, hit enter
// it will take a couple of minutes (around 3-5min in my case)
// watch the tablet for success message, it should be displayed there if everything works
// but also, watch your terminal...if it gives you error message similiar to:
// ==> [I][U]failed with error message that it can't write somewhere[/U][/I]
// you have to try with brick-9820 script

sudo ./brick-9820.sh
// it will take a couple of minutes, similar to above step

NOTE

: after either of the above commands (which one succeeds) POWER OFF THE TABLET and DO NOT try to turn it back on. It should stay powered off!!

sudo ./bootrom-step.sh
// this will take some time (in my case around 5-10 minutes)
// will give you message similar to "awaiting device connection" and nothing else...
// although nothing seems to happen, just wait a bit and watch the terminal, it will soon start displaying the process
// it should then reboot the tablet, but in my case, that did not happen, so i had to do it manually...
// NOTE that althought tablet seems to be "off", it isn't, so press power btn and hold for 5 sec to turn it off
// after that click and hold volume up button (when in portrait mode it is the right one, the one closest to power btn)
// and immediately after that press and hold the power btn until amazon logo shows itself
// it should then show in bottom left corner HACKED FASTBOOT after a few seconds

sudo fastboot devices
// there should be a device listed
// if not, you should run (in the extracted directory that you are in):
./bin/fastboot devices
// if sudo fastboot devices does not show your device but ./bin/fastboot works, you have to edit the fastboot-step.sh file and change the fastboot commands to ./bin/fastboot

sudo ./fastboot-step.sh
// takes a couple of minutes (1-3 min in my case)
// reboots the device

after that you should be in TWRP :)

NOTE when in TWRP:

DO NOT RESTART tablet before the following

(or amazon fire os will overwrite TWRP and you will be reset to factory default with fireOS, losing everything you've done and starting from scratch...

when it happened to me, the brick-9820.sh didn't work anymore and had to use brick.sh script)

-allow modifications

-format data,system,cache partitions, go to wipe->advanced wipe-> repair/format (something like that), select each of the 3 partitions aformentioned and format to ext4

-if you've done it correctly, there should not be any red warnings

-after that go to wipe, select all partitions and wipe them (just to be sure)

-tablet should be connected and TWRP should be left on

on PC

-download Lineage 12.1 ROM from https://xdaforums.com/hd8-hd10/general/discussion-root-progress-fire-hd-8-t3743024

-download opengapps from https://opengapps.org/

- put them inside amonet-douglas-v1.2 folder where you've extracted the prior ZIP files (just to be clear, you can put them anywhere, but i like to keep it all inside the working directory)

-go to terminal

adb push lineage-12.1-20200614-UNOFFICIAL-douglas.zip /sdcard
adb push open_gapps-arm64-5.1-nano-20200624.zip /sdcard

now the files are on the tablet

- in TWRP go to INSTALL, go to /sdcard folder if not in it

- first install Lineage ROM from zip

- then install GApps from zip

hope it works!

I'm glad i've finally rooted it, thank you all for the great content here! :)