[BRX]

If I remember correctly I didn't even sideload (with USB/ADB) but used this simpler way (also by XDA http://forum.xda-developers.com/amazon-f...e-t3216122 Post #4):

Download ES File Explorer from the Amazon Marketplace. It's free.

Allow Apps from Unknown Sources
Settings>Security>tap toggle>Ok

Download https://mega.nz/#F!AI5n0AaR!Qw-WJrBoCP8bce-so0hzFQ
place on sd card

Install these files
Google Play (com.android.vending-5.9.12-80391200-minAPI9.apk)
Google Play Services (com.google.android.gms-6.6.03_(1681564-036)-6603036-minAPI9.apk)
Google Account Manager (GoogleLoginService.apk)
Framework (GoogleServicesFramework.apk)

open with file manager
file manager will ask if you want to install

Rebooting is a good idea.

most likely you will need to grant special permissions for Google Play services
with an adb command see post #2

Done.