[Fire HD 8 and HD 10 Original Android Development] kingladar:
I also bought several of the 7th gen devices from Woot. Here are my instructions for loading Lineage 15.1. They are based on what pug_ster provided, with typos fixed, and precise commands to run.

1) Boot using Fedora. See notes below if you're using Ubuntu.

2) Prep and install tools.

sudo dnf install -y android-tools dos2unix python3 python3-pyserial unzip
sudo systemctl disable ModemManager && sudo systemctl stop ModemManager
curl -L -s -o brick-douglas.zip https://xdaforums.com/attachments/brick-douglas-zip.4825253/ && unzip -qq -e -d brick-douglas brick-douglas.zip
curl -L -s -o amonet-douglas.zip https://xdaforums.com/attachments/amonet-douglas-v1-2-zip.4845269/ && unzip -qq -e -d amonet-douglas amonet-douglas.zip
curl -L -s -o lineage-15.1-douglas.zip https://github.com/mt8163-dev/android_device_amazon_douglas/releases/download/15.1-8.0/lineage-15.1-20211107-UNOFFICIAL-douglas.zip
curl -L -s -o open-gapps-arm64-8.1-pico.zip https://jaist.dl.sourceforge.net/project/opengapps/arm64/20211217/open_gapps-arm64-8.1-pico-20211217.zip
md5sum lineage-15.1-douglas.zip > lineage-15.1-douglas.zip.md5sum
md5sum open-gapps-arm64-8.1-pico.zip > open-gapps-arm64-8.1-pico.zip.md5sum
echo 6647dd0b5b9d2c04a2f167f6ccc7a2cfbcaa6f1f93f8251c7a39455db77119b2 amonet-douglas.zip | sha256sum -c
echo ba017f1c4fc2f003924912a9099d18c94dd82401a2ad12881b7e7e158a4bc06b brick-douglas.zip | sha256sum -c
echo 4351859b45eb5124d4ed6ddf4f32cbd29ef61adfa79574208a408926f431db46 lineage-15.1-douglas.zip | sha256sum -c
echo 8bb21f299a77c535f8aad39d7b4fdd25966daa143f6fa06a2ac2eb274c2daba7 open-gapps-arm64-8.1-pico.zip | sha256sum -c

3) Reboot Fire HD 8 into recovery mode.

Power off the device, then press the Volume Down + Power keys until the Amazon logo appears.

4) In recovery mode run Factory Reset followed by Wipe Cache and then reboot to Bootloader.

A black screen with "Fastboot" in the lower corner should appear.

5) Connect the tablet to a computer using a Micro USB cable and run the brick script. This will brick the tablet.

cd brick-douglas/amonet
sudo ./brick.sh

6) If Display reads "Disconnect USB and Powerdown" message, proceed to step 7. Otherwise if the tablet reboots into FireOS, repeat steps 3-4, and use the alternate brick script.

cd brick-douglas/amonet
sudo ./brick-9820.sh

7) Assuming you've reached the "Disconnect USB and Powerdown" message, long press the power button to shutdown, and then disconnect the tablet.

8) Run the bootrom script, and then connect the bricked tablet. Allow the script to complete.

cd amonet-douglas/amonet

sudo ./bootrom-step.sh

9) Use the fastboot script to install TWRP which will reboot the tablet into recovery mode when it's complete.

cd amonet-douglas/amonet

sudo ./fastboot-step.sh

10) Prepare a Micro SD card and load the following files onto it, and insert the card into the tablet.

lineage-15.1-douglas.zip

open-gapps-arm64-8.1-pico.zip

lineage-15.1-douglas.zip.md5sum

open-gapps-arm64-8.1-pico.zip.md5sum

11) Swipe the slider to enable modifications. Then from within TWRP, run the following actions to create a data partition and mount the SD card.

Wipe -> Wipe Data -> Yes

Mount -> Advanced Mount -> Select the Partitions

System

Cache

Data

Storage

Install -> Select Storage -> Storage -> Select Files

Select lineage-15.1-douglas.zip

Add More Zips

Select open-gapps-arm64-8.1-pico.zip

Swipe to Install

12) When the installation is complete, remove the SD card, and wipe the Dalvik cache, and press reboot.

13) Enjoy your Amazon+Google subsidized device.

Notes)

On Ubuntu replace the DNF install command with the corresponding APT command below.

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

For the privacy inclined, omit the open-gapps-arm64-8.1-pico.zip file from 11 for a Google-free device.

To cleanup the downloaded files run the following.

rm -rf amonet-douglas amonet-douglas.zip brick-douglas brick-douglas.zip lineage-15.1-douglas.zip lineage-15.1-douglas.zip.md5sum open-gapps-arm64-8.1-pico.zip open-gapps-arm64-8.1-pico.zip.md5sum