[Kindle Fire HDX 7" & 8.9" General] slvr32:
Davey126's FireOS v4 vs custom HDX ROM distinction is exactly right, and I didn't mean to steer this thread to an off-topic tangent, but I also don't mind explaining what I've done with my own HDX 7 (thor).

I also happen to have a 4th gen HDX 8.9 LTE AKA Saturn tablet, so I'm familiar with how much easier it is to get a more functional Google Play Store experience on FireOS v5 vs FireOS v4, without any rooting (my Saturn tablet isn't rooted, and is running the latest FireOS 5.3.1.1 release, but I really prefer FireOS 4 over FireOS 5 on the HDX tablets).

In any case, my HDX 7 now (w/FireOS 4.5.5.2) only has enough Google components (Play Store, Play Services, Account Manager, Services Framework) to make a relatively small number of apps happy, and the Play Store isn't really functional, but the other Google bits are at least functional enough to allow me to add multiple Google accounts (personal and corporate), and also an Exchange account (via the stock Email app on the HDX), so that I can at least view calendar events for these three accounts in the same Google Calendar app.

I did try using the root + HDXposed module route earlier, as I hinted at a few posts ago, and that certainly gives you a more functional Google Play Store, but you quickly encounter issues w/compatibility once Google Play Store and Google Play Services are quietly upgraded (Google Play Services 9.8.77 vs 10.0.84 is the real problem), so I opted to go back to a slightly less functional Google Play Store (w/Google Play Services 9.8.77) that I was already familiar with, before my HDX was rooted or had an unlocked bootloader.

Generally speaking, my FireOS4 install leverages the 1Mobile Market app, for paying attention to app updates, but some updates come with a bit of trial and error, where most recently, some recent Google apps (Docs and Sheets) want Google Play Services 10.0.84, but as I mentioned earlier, 10.0.84 creates apparent latency and other issues with various apps on FireOS 4.

Again, I'd really prefer to put this FireOS 4 tangent to bed, for the sake of not derailing this thread, but I have the following apps working, considering my earlier disclaimers, but also keep in mind that I also generally turn off almost all notifications, since many things are really only suited for manual checking, since the semi-functional Google stuff really cripples notifications.

It's easiest for me to list these alphabetically (more or less), as I'm looking at one of my Google Drive folders with all of my side-loaded apps (I maintain backups of these with App Backup & Restore)...

Some of these apps are listed with redundant Google names, to avoid ambiguity with other apps with similar names...

(and please excuse any app versions that aren't exactly correct as I'm transcribing them)

1Mobile Market 6.6.9.6

Amazon Drive 1.7.0.17.0

App Backup & Restore 6.0.6

BeyondPod 4.2.16

Bookshelf 3.9.1

Duo Mobile 3.15.0

ES File Explorer 4.1.5.4

Facebook 106.0.0.26.68

Firefly 1.6.22.1 (nice to have, works on HDX 7, even though the HDX 7 only has a front-facing camera, grabbed from my HDX 8.9 at some point)

Google Account Manager 4.0.3-239410

Google App 6.1.28.16

Google Calendar 5.3.8

Google Chrome 55.0.2883.91

Google Docs 1.6.482.10.35

Google Drive 2.4.452.14.35

Google Gmail 6.7.12.8801648

Google Hangouts 15.0.141104777

Google Maps 9.33.1

Google News & Weather 2.9.2

Google Play Services 9.8.77

Google Play Store 4.6.17

Google Services Framework 4.0.4-33869

Google Sheets 1.6.482.10.35

Google Snapseed 2.14.0.141187073

Google Voice 0.4.7.10

Google YouTube 4.1.781

Merriam Webster Dictionary 3.3.1

Facebook Messenger 100.0.0.29.61

Mint 5.0.1

Moboplayer 1.3.214

MX Player 1.8.15

MX Player Codec ARM v7 Neon 1.8.12

Netflix 3.16.3.5359

Redfin 112.2

Skype 7.30.0.1372

Slack 2.26.1

Snapchat 9.42.2.0

Starbucks 4.3.2

Yelp 7.10.1

I actually have all of these apps backed up in a Google Drive folder, but I also have a couple of things (actually, just my own BeyondPod license key and a couple of other apps) that aren't appropriate for a wholesale share of the related Google Drive folder

I also have the Swype keyboard installed from the Amazon Appstore, but I generally side-load apps, rather than grabbing anything from the Amazon Appstore, in all of the list above.

Finally, I have Xposed 2.6.1 installed, but I only have the App Settings and XInsta modules installed.

Also, for Snapchat, you have to consider the usual caveat of recent Snapchat not wanting to see a rooted device and/or Xposed, so you want to log in to Snapchat before you root the tablet and/or install Xposed.

A lot of the above is just trivia, and really belongs in another related thread, and it's not meant to inspire support for these items on FireOS 4.

I've personally also had 2012 Nexus 7, 2013 Nexus 7, Nexus 10, Nvidia Shield K1, and Fire HDX 8.9 LTE tablets, and I currently have a OnePlus X phone w/CM13. but my HDX 7 LTE has outlasted both of the Nexus 7 tablets, and I use the HDX 7 and HDX 8.9 tablets ever day.

Funny thing, I actually just bought a used 3rd gen HDX 8.9 LTE tablet yesterday (haven't received it yet), mostly because I recall FireOS 4. having a much more stable LTE connection than FireOS 5 (w/FireOS 5, you often lose the LTE connection when the tablet wakes up from sleep, and you have to reboot the tablet, when toggling the data connection off/on doesn't fix it, which is very annoying), and I accidentally upgraded the 4th gen HDX 8.9 LTE a few months ago, when I mistakenly flashed a FireOS 5.3.3.1 package that I thought was FireOS 4.5.5.2, shortly after my HDX 7 got the 4.5.5.2 update.

I used to have a 3rd gen HDX 8.9 LTE tablet (Apollo) before I bought my current 4th gen HDX 8.9 LTE, so some of these recollections and experiences go back as far as 2013 for overlap between the HDX 7 and the 3rd gen HDX 8.9 LTE.

It just happens that my LTE data plans for my tablets only cost me $10/mo each to match up to 5GB of data on my cell plan (old T-Mobile plan they no longer offer), and I previously had a Nokia N9 (one-off linux-based phone, not to be confused with Android, or Symbian, or Windows Phone) phone, and only switched to an Android phone for the first time ~ a year ago., but I really don't like any Apple stuff, beyond the fact that OS X (recently rebadged as macOS) is mostly a pretty Unix-like system (actually more of a NeXT evolution, than an evolution of legacy MacOS, and most Mac users don't know or care), and I happen to be a Unix administrator w/a CS degree.