[Fire HD 6 and 7 General] DoLooper:
[EDIT Oct. 25] Here's what I did--cleaned up and corrected for bootloaders--to install the official 5.2.2 update (build date September, 2015) on myrooted tablet running Developers Preview, build date July, 2015.This is only for those who rooted and installed the dev preview before the upgrade/downgrade troubles. It let's you keep all your stuff.

Few important things:

If you don't reset/wipe in TWRP you can keep most of your stuff, including homescreen layout, play store and all apps. However . . .

Google framework, account manager, contact sync and calendar sync get deleted with the update.

I didn't flash Gapps and got bogus insufficient space error [130 Mb free] when I tried later. Restoring framework fixed everything, but it may be best to flash new Gapps (although that can cause problems when update doesn't completely wipe /system, like this one). :p Up to you.

Oct 26 Update: Based on reported "insufficient space" flashing Gapps--plus testing and researching contacts and calendar--I suggest not flashing Gapps but simply backing up Google services framework before you upgrade and restoring it after. The other google system apps that get deleted don't seem to be needed; if you want to sync Google contacts & calendar on the Fire you can add your google account(s) in Settings, same as on any Android. If you don't want Amazon's stock calendar or contacts, get another from the Play Store. I've updated the instructions to reflect this.

.

HDXposed module is no longer needed for working Play Store.

Xposed Framework: The update doesn't support the version we used with the July dev preview. You must either flash the latest version or flash the uninstaller if you don't want Xposed anymore.

Stock launcher now = com.amazon.firelauncher

Home key now defaults to stock launcher until you pm disable it. (No prompt anymore)

Backup Google Services Framework.

Turn off wifi (airplane mode) and plug in.

Download the zips:

* September 5.2.2 update (thanks @Hariiiii !) and rename extension from bin to zip.

update-kindle-full_ariel-20.5.2.2_user_522053520.bin: https://mega.nz/#!ZI1wTL6L!xbDNDvaJjLUWwqe8J9awAs4xNQvxreXCmZ1I6cWTLVA

* Latest Xposed Installer or Uninstaller from here: http://xdaforums.com/xposed/super-alpha-posted-permission-xposed-t3072979

Installer = Xposed-v74-sdk22-arm-by-romracer-20150911.zip

Uninstaller = xposed-uninstaller-20150911-arm64.zip

* Gapps (if using)

tk_gapps-modular-pico-5.1.1-20150920-signed.zip: http://xdaforums.com/android/software/tk-gapps-t3116347

* 5.2.0_stock_recovery_only.zip

Attached to bibikalka's lollipop post: http://xdaforums.com/fire-hd/general/how-to-upgrade-to-lollipop-root-gapps-t3163950

Get latest SuperSU apk (?) Don't know if it's required, but I installed it.

- SuperSU 2.52 Beta: http://www.apkmirror.com/apk/chainfire/supersu/supersu-2-52-android-apk-download/

Follow Step 1 of @bibikalka's guide to temporarily install TWRP and while in TWRP:

a. Flash the update

b. Flash Xposed (installer or uninstaller)

c. Flash 5.2.0_stock_recovery_only.zip

d. Choose boot to recovery and install SuperSU when TWRP prompts you.

Confirm you're in recovery, then boot to system and press Exit at "Welcome to Fire OS 5!"

In OS, see if SuperSU is still managing root access. If it's not or you want to update, install the new SuperSU apk and update binaries.

(Wait to reboot unless you can't get su access at next step.)

Block OTA:

a. Disable dcp or otaverifier (whichever you prefer)

b. Rename system/priv-app/devicesoftwareota/devicesoftwareota.apk extension to apk_

Restore Google Services Framework and reboot.

Turn on wifi and sign in to playstore.