[Fire HD 8 and HD 10 General] bakshi:
I've finally managed to destroy all of the Google glitches on Fire OS after much troubleshooting and many factory resets. This guide will show you how to permanently fix the following issues:

Gmail closing after right after opening

Google Contacts not pulling your contacts

Google Calendar not pulling your calendar

This requires some patience.

Reported Bugs:

Gmail crashes when opening an attachment in an email and some users are speculating it's the Amazon Download Manager causing the crash. I'm looking into it.

Requirements:

Root (This easy guide shows you how to root your 7th generation Fire HD)

Fire OS 5.6.0.0

Fire HD (2017)

ADB (Optional, this 'Lite' package is officially provided by Google)

Basic knowledge of ADB commands

Downloads:

Google Account Manager (You have to download this specific one since it's the last one compatible with Lollipop!)

Google Services Framework (You have to download this specific one since it's the last one compatible with Lollipop!)

Google Play Services (It's okay to download the latest version!)

Google Play Store (It's okay to download the latest version!)

Google Calendar Sync (You have to download this specific one since it's the last one compatible with Lollipop!)

Google Contacts Sync (You have to download this specific one since it's the last one compatible with Lollipop!)

Link2SD

Titanium Backup

Gboard

Step 1: Enable install of "Apps from Unknown Sources":

Go to Settings > Security and enable “Apps from Unknown Sources”. This will allow you to sideload the Google APKs that you'll need in order to install the Google Play store onto your Fire HD.

Step 2: Download and install these APKs in sequence: (I've included their package names below so they are easier to locate in the Fire HD Docs app!)

Google Account Manager - com.google.android.gsf.login

Google Services Framework - com.google.android.gsf

Google Play Services - com.google.android.gms

Google Play Store - com.android.vending

Google Calendar Sync - com.google.android.syncadapters.calendar_5.2.3-99827563-release-2015080710_minAPI15(nodpi)

Google Contacts Sync - com.google.android.syncadapters.contacts_5.1.1-1965118-22_minAPI22(nodpi)_apkmirror.com

Step 3: Setting up Google Play & downloading applications:

Open Google Play Store and login to your Google account

Download all of your Google applications like Gmail, Gboard, Calendar, Contacts, Photos, Rewards, and etc.

Don't setup Gmail just yet

Make Gboard your default keyboard by disabling Fire Standard Keyboard - adb shell pm disable com.amazon.redstone

Download Link2SD

Download Titanium Backup

Step 4: Extra Gmail steps: (This is temporary until the crashing bug has been eliminated)

Open Gmail but don't do anything else yet

Set Fire HD to "Airplane mode" or just disconnect from wireless

Now go to your Gmail Settings

Choose your Gmail account in the next page

Scroll down to Data Usage and uncheck "Download attachments"

Set Days of mail to sync to 10 days

Step 5: Avoid any bootloops by eliminating this potential roadblock with Titanium Backup or ADB:

adb shell pm disable com.amazon.redstone

Step 6: Now you're going to need to free up some space within the /system partition. Remove these applications via Titanium Backup or ADB:

Kindle Special Offers - adb shell pm uninstall com.amazon.kindle.kso

Kid's Silk Web Browser - adb shell pm uninstall com.amazon.cloud9.kids

Fire Keyboard (Asian) - adb shell pm uninstall jp.co.omronsoft.iwnnime.mlaz

Calendar - adb shell pm uninstall com.android.calendar

Contacts - adb shell pm uninstall com.android.contacts

Fire Tutorial - adb shell pm uninstall com.amazon.kcp.tutorial

Fire Keyboard Simplified Chinese Pack - adb shell pm uninstall jp.co.omronsoft.iwnnime.languagepack.zhcn_az

Amazon Retail Demo - adb shell pm uninstall com.amazon.kor.demo

Home Screen Tips - adb shell pm uninstall com.android.protips

Music - adb shell pm uninstall com.android.music

My Videos - adb shell pm uninstall com.amazon.kindle.personal_video

Amazon Cloud Photos - adb shell pm uninstall com.amazon.photos

Weather - adb shell pm uninstall com.amazon.weather

Email - adb shell pm uninstall com.android.email

Amazon Cloud Photos Importer - adb shell pm uninstall com.amazon.photos.importer

Kingsoft Office Bull**** - adb shell pm uninstall com.kingsoft.office.amz

Step 7: Open up Link2SD and go to User Applications. Convert the following apps into system apps:

Google

Google Play Store

Google Contacts

Google Contacts Sync

Google Calendar Sync

Step 8: Last step:

Reboot through Link2SD or ADB. All Google apps should function normally afterwards.

Sources:

https://www.howtogeek.com/232726/how-to-install-the-google-play-store-on-your-amazon-fire-tablet/

https://xdaforums.com/amazon-fire/help/gmail-app-kicking-closing-t3607306

https://xdaforums.com/hd8-hd10/help/google-mail-app-crashes-time-update-t3594701

https://xdaforums.com/kindle-fire-hdx/help/gmail-app-stopped-kindle-fire-hd-8-gen-6-t3588914