[stumped]

apps are locked to the account that bought them. if you try to move via backup & restore to a device registered to a different account, then the licence check fails. Been there, tried that.. and the licence checks seem to repeat daily, in most cases.
I am slowly replacing our amazon app store apps with the google equivalents anyway, as amazon's are so out of date- e,g, the .uk ebay app is about 3 years behind the google equivalent & has some broken features. Flipboard ditto & flipboard tell me they have quit updating the amazon version.

"bought" Video is only visible to the purchased account. I am not e sure if you can share it via the new fangled " family share"
we have the older prime set up where i registered 4 accounts to share the prime shipping benefit, but that is all that is shared.
I only "buy" video with no-rush credits, not with real money, because of it being not really " owned". plus much of the instant video pricing takes the p**s, and often exceeds the cost of a physical better quality blu ray copy.