Couldn't find any existing guide for this so figured I'd add one. Approach probably applies to other Fire Tv Apps as well.
I used adb to pull the NBC Sports apk from my fire tv. I pulled Amazon appstore from my android phone.
I uploaded both here
NBC Sports App http://s000.tinyupload.com/?file_id=29137188811659130883
Amazon App Store http://s000.tinyupload.com/?file_id=94491635617393954099
Use whatever approach you're used to for sideloading both apks on your Android Tv. You then need to log into Amazon on the Amazon Appstore app. On my Shield Tv, I needed to use the controller to control login.
After that I used TvAppRepo to generate a shortcut for NBC Sports. Seems to work exactly the same as the Fire TV App.
Thanks for the easy Amazon sideload. :)