Please note: This little trick still works, however if your tablet runs FireOS 18.104.22.168 or greater, you will NOT be able to uninstall Amazon's contact app.
This neat little trick deserves it's own thread. While you have to uninstall two Amazon system apps, you actually gain the use of other built in FireOS features as a result. If you still have all three Amazon Contacts apps enabled on your tablet, you're able to use this little customization. If not, you'll have to factory reset, as I'm not sure Google Contacts will work properly. You must also have Google Play, Google Account Services, Google Framework and Google Play services installed. You have to install the Google App as well. Please install Activity Launcher as well.
There is very low risk of doing any damage whatsoever to your device, but I feel obligated to say: I can't be responsible if you don't have the same results. So if something does go bad, the worst possible case is a factory reset.
1) Download and install Google Contacts 1.1. You can now export your contacts from a Android device. Just copy them to any storage as a vCard, .vcf etc. Then copy that to the storage of the device you want the contacts list. You can also port it over to your target device's storage using Google drive or Bluetooth.
2) Open Google Contacts and import the file from the storage directory you saved it in. You now have all your contacts. Now download and install Google Contacts Sync 5.1.1-1965118. Go back to Google Contacts. They should be syncing and you should now have more options available to you in Contacts settings. Surprisingly Contacts Sync also assists in syncing portions of your Google account as well as I show below.
3) In contacts, you should see an option to set your profile up. Tap it and Upload a picture and add some information. Tap the arrow in the top left when done, it will save automatically.
4) Open Activity Launcher and tap the top left, all activities. Scroll down to Settings and tap it. Scroll to Users and tap it. You should see a screen similar to the one below; a 'profile' with the picture you saved in Contacts
5) Tap on the profile and give yourself a nickname and tap save. Making sure everything is saved, tap the recent apps button (square) and swipe it all out. Now press the power button so it locks your device. You just want to activate your lock-screen. Press it again to turn it back on and look in the top right of your lock screen. Tap on it.
6) Unlock your tablet. Swipe down the status bar all the way. Look at the top right corner. Tap on it a few times.
It was really fun to have found this. I'm glad I finally found a trick that didn't involve nuking more of Amazons apps or functions. Note that both of their contacts apps are 100% android based, so technically were not nuking anything that is directly related to FireOS.
What's even better? It ALL holds after rebooting I don't think the 'profile' does much of anything except look cool and expands a little to show your nickname. If you do find other functions for it, please let us know Though I think the way my device is setup currently, this is just a little bit of fun customization.
P.S. If anyone has a problem with the shirtless picture, I'll upload new ones.
EDIT: You can manually uninstall Amazon Contact app and the Amazon Contact Sync app. **DO NOT UNINSTALL AMAZON'S CONTACT STORAGE APP.** Doing so will result in your contacts not working at all. So far I've yet to find a fix, but it's really not necessary.
If a more automated version suits you and check out the Amazon Fire Utility and see if it's right for you
***UPDATE September 1, 2017:*** Google has released their contacts app to be compatible with all Android devices running 5.X and above. You can go to the Play Store and update the app here. You MUST KEEP the contact sync app if you already have it. The little bit of customization as a result of adding contacts, remains the same I believe. Just tap 3 bars at top left > settings > tap your name > set yourself up. I just flashed Fire Nexus to my Fire 7 and the process was still applied. I am not sure why it just doesn't add your picture already associated with your Google Account (if you already have one selected).
If most of your contacts have been duplicated after updating contacts app, go to your google Contacts page on the web and look at the menu on the left. If there isn't one, tap the 3 bars at top left and select duplicates. That will bring up all your duplicate contact names. Then select 'merge all' which will merge them together including the info.
You can no longer uninstall Amazon apps if you are on FireOS 22.214.171.124 or greater.