[Kindle Fire HDX 7" & 8.9" General] Luxen:
After this little adventure, I went into further testing. There is now a much simpler method of installing the Google Play Store. Fully functional. Two methods to be exact, and an experimental one.

Method 1) -

Recommended if you have Safetrap 4.01

Make sure you have SuperUser (Not tested with Kingroot)

and you are running 4.5.5.1 (It'll probably work in earlier versions.)

Note: I have Superuser installed as a system app for safety.

My device is a Kindle Fire Hdx 7" (3rd gen) Thor.

-You need Safetrap (or head to method 2 for a non safe-trap procedure)

-You need to be rooted

-And you need to download from Open GApps (Platform: ARM Android: 4.4 Variant: Pico < Smallest package)

First, you must make space in

System/Priv-app

to flash this little package. (< There's no way around this)

I deleted [ moffice, weather, and the android.mail.apk ] (I do not need those. I actually do not need a lot of the amazon services except for books.)

Reboot into Safetrap and flash/Install the opengapps package.

Wipe Dalvik/Cache. Reboot

> If you get a "Failed" - It means you need to delete more apps.

Make sure the message reads

"Insufficient space, etc" and not

"incompatible,"

If you are successful, reboot.

Open the Google Play Store and simply sign in with your account. You are done.

I haven't experienced any crashing. nada.

Use Market helper for incompatible app (Although inbox by gmail isn't working for me, everything else is.)

Method 2) Recommended if you don't have Safe trap.

You might need to delete some apps from

system/priv-app

if you get "Insufficient space error" <For me, I didn't have to delete anything.>

You do not need Safetrap

.

-You need Root and you need to follow the method described here, but with a little tweak:

Move all the apps mentioned in the guide to System/Priv-app > Account And Sync Settings, Google Services Framework, Google Login Service, and Vending.apk)

Install Google Play Services from your downloads (Normal Install)

< I am using the latest ones I got off Google.>

Reboot.

Open the android market (in apps) and sign in. <

Download the latest Google Play Store (from the guide or Google)

I renamed it vending.apk for short.

Delete the vending.apk found in System/Priv-app and replace with the new one.

Reboot.

Google Play Store is functional and shouldn't crash.

--------------------------

(I highly recommend a Custom ROM.

The quality and functionality can not be beaten.

.)

Update: Now that the kindle app on android supports exporting highlights from personal docs/side-loaded books, etc.. I've made the full switch to CM11 :)

------

Not recommended.

The method below is now experimental. I couldn't get it to reproduce after replacing Kinguser With SuperSu.

This is a fully functional Playstore. You can search, download and update :)

Tested on:

Kindle Fire HDX 7" (3rd Gen) running 4.5.5.1 w/ Kingroot

* No one is more responsible for your device than you. With that in mind, back up, read carefully, don't go the extra mile just because, and be aware there is always a risk. On to the fun stuff~

You will need:

-Root

-Safetrap v4

-All 4 apks from here (Skip all the instructions there and scroll to where it says —Then install these apks—

You also need the Google Apps Minimal Edition from here.

----INSTRUCTIONS

-Move all 4 apks to sdcard/download and install each one.

-Move your Google Apps Minimal Edition.zip to sdcard/download and keep it there.

Reboot into Safetrap.

* Make sure you have a backup of your STOCK Rom !

Go to Install > Find your Google Apps Minimal Edition.zip and install it.

From the same screen once you are done wipe dalvik/cache

Reboot.

You might run into a gray screen ? Hit the home button. It is a one time thing.

Login to your existing Google account. You'll notice the App Store will crash after a minute.

Reboot. That's it. Playstore shouldn't crash anymore.

#If it works for other devices, versions, let me know. Thank you.

I tested it on my own device, and downloaded a couple of apps. If something changes I will update this.

Update: You can find the latest Google Play Store and Services here. Uninstalling both items is necessary to install the new version then you can use ccleaner to remove any Google app that says 'newer version installed'