You need to look at the license agreement first. They are for personal use ans one can get in trouble if showing video at a public place. If your workplace has lawyers, you should check with them if you have already been playing videos to clients. Those same kinds of viewing laws apply to dvds, blurays, or any copy of videos and movies. Places such as medical facilities who show videos to patients, even in waiting rooms have to purchase special viewing licenses to avoid heavy fines if caught otherwise.
See here for which devices you can download Amazon/Prime Videos to (you do know you are just purchasing a license to view/access them, not the actual video, right?):
Prime Video Devices & Features
Ther useful links: Amazon Prime Video Terms of Use
h. Limited License to Digital Content. Subject to payment of any charges to rent, purchase, or access Digital Content, and your compliance with all terms of this Agreement, Amazon grants you a non-exclusive, non-transferable, non-sublicensable, limited license, during the applicable Viewing Period, to access and view the Digital Content in accordance with the Usage Rules, for personal, non-commercial, private use.
Conditions of Use
LICENSE AND ACCESS
Subject to your compliance with these Conditions of Use and any Service Terms, and your payment of any applicable fees, Amazon or its content providers grant you a limited, non-exclusive, non-transferable, non-sublicensable license to access and make personal and non-commercial use of the Amazon Services. This license does not include any resale or commercial use of any Amazon Service, or its contents; any collection and use of any product listings, descriptions, or prices; any derivative use of any Amazon Service or its contents; any downloading, copying, or other use of account information for the benefit of any third party
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