Can I stream Amazon Prime or Netflix videos in my classroom?
No.
You do have access to Discovery Education and TeacherTube for educational videos. See the links under Teacher Resources.
At this time Netflix cannot be used in a classroom due to legal issues. Per their user agreement, they only allow videos to be viewed for personal use.
Many schools have brought the issue up with Netflix and their response has always been that it is not considered personal use when used by schools and/or libraries.
There is also no "commercial/enterprise" licensing available for say a "school" registered account at this time.
Amazon grants you a personal, non-exclusive, non-transferable, non-sublicensable, license, during the applicable Viewing Period, to access, view, use and display the Digital Content in accordance with the Usage Rules, for Non-Commercial, Private Use. "Non-Commercial, Private Use" means a presentation of Digital Content for which no fee or consideration of any kind (other than that which you pay to us to view the Digital Content) is charged or received, which takes place in your private home or apartment or, if outside your private home or apartment (e.g., in a hotel room, dorm room, office, or airport waiting lounge) is limited to a private viewing for you and your invitees. Non-Commercial, Private Use specifically excludes any public presentation (e.g., a presentation in a dorm lounge) and any presentation by a place of public accommodation or other commercial establishment (e.g., a bar or restaurant), even if no fee is charged for viewing the Digital Content.