Bypassed the Amazon App Store
Used the process listed below in a post and it worked great, you just have to remember to select the ".APK" file, the apps do show in the Kindle Fire "App" screen and I was able to add them to "Favorites"
Apps downloaded, installed, and tested successfully:
..Gospel Library
..LDS Tools
..TeamViewer Mobile App, TeamViewer 7.0.238 (Pro) Lic: free
Note: Kindle Fire install setting, tap the top right part of the screen, then Click "More...", then "Device", scroll to "Allow Installation of Application" change setting from "Off" to "On", accept the message. After the install, you may want to change "Allow Installation of Application" back to "Off"
Test Kindle Fire's 'Silk' Browser which uses Amazon’s EC2 cloud computing cluster
lds.org/Tools
..Calendar - works
..Directory - works
..Maps - works (make sure "Load images" setting is enabled)
speedtest.lds.org - worked somewhat
..(only speed test worked because "Java not Detected" and you must turn off "Accelerate page loading")
speedtest.net - worked (you must turn off "Accelerate page loading")
Thanks,

Your Fellow Member,
Pete Arnett
Sunny South Florida, USA