[Fire HD 8 and HD 10 General] retyre:
You will find a FlashFire-flashable prerooted 5.6.3.0 image (boot and system) in the link at the bottom. Before we get there:

What you are liable for:

-- Everything

What I am liable for:

-- Nothing

What the .zip in the link contains:

-- Boot image from 5.6.3.0 (you can extract this from the update .bin)

-- Prerooted 5.6.3.0 system image with (a) the su binary, Xposed framework, and busybox, (b) renamed DeviceSoftwareOTA.apk, and (c) edited build.prop with 987654321 as the build number

What this does not contain:

-- SuperSU, FlashFire, Xposed Installer, any other app that's not Amz-stock

-- The goal of this exercise is not to provide user-installable apps (like the aforementioned, different launcher, etc.) that users can install on their own. Bear in mind that many of the user-configurable options (e.g., disabled packages) reside in /data.

What you should do before flashing:

-- Move some apps (traditional /data apps that you may have converted to /system apps) to /data/app/ if you have not already done so

-- Make a FlashFire backup of your current setup

How you should use this:

Method #1:

-- Extract the contents of the archive to a folder

-- Extract boot and system from the respective archives (boot.gz and system.gz); optional: rename the images to boot.img and system.img

-- Flash boot.img and system.img (as firmware images) using FlashFire (requires busybox date hack or Xposed and hoop-jumping)

Method #2:

-- Extract the contents of the archive to a folder in /sdcard/FlashFire/Backups/

-- Restore using FlashFire (requires busybox date hack or Xposed and hoop-jumping)

-- I'm finding v0.24 to be more reliable than v0.51 when it comes to restoring (esp. data)

Why you should try this:

-- No reason

What you should do after you try this:

-- Post your findings in this thread (esp. what doesn't work in 5.6.3.0 that did in 5.6.2.0/5.6.1.0/5.6.0.1)

5.6.3.0

You will find the 5.6.2.0 boot.img and system.img in the link at the bottom. Before we get there:

What you are liable for:

-- Everything

What I am liable for:

-- Nothing

What the .zip in the link contains:

-- The boot.img from 5.6.2.0 (you can extract this from the update .bin)

-- Prerooted 5.6.2.0 system.img with (a) the su binary, Xposed framework, and busybox, (b) renamed DeviceSoftwareOTA.apk, and (c) edited build.prop with 987654321 as the build number

What this does not contain:

-- SuperSU, FlashFire, Xposed Installer, any other app that's not Amz-stock

-- The goal of this exercise is not to provide user-installable apps (like the aforementioned, different launcher, etc.) that users can install on their own. Bear in mind that many of the user-configurable options (e.g., disabled packages) reside in /data.

What you should do before flashing:

-- Move some apps (traditional /data apps that you may have converted to /system apps) to /data/app/ if you have not already done so

-- Make a FlashFire backup of your current setup

How you should use this:

-- Flash the two images in FlashFire (requires Xposed and hoop-jumping)

Why you should try this:

-- No reason

What you should do after you try this:

-- Post your findings in this thread (esp. what doesn't work in 5.6.2.0 that did in 5.6.1.0 or 5.6.0.1)

5.6.2.0

5.6.1.0