Answer: Yes, but only for some titles.
Certain Netflix Original Documentaries bear a "Grant of Permission for Educational Screenings". These documentaries are the only content on Netflix that is expressly permitted to be shown in settings like a classroom or school club. An example of such documentary would be "Cuba and the Cameraman".
Any title without this Grant of Permission cannot be streamed in the classroom without violating Netflix's Terms of Service. This is a vast majority of the content on Netflix! While it may seem like you should be able to claim fair use when streaming content in the classroom, this is less of a copyright and more of a licensing issue, and Netflix reserves the right to enforce its license agreement that you agreed to when you signed up for your account.
Hulu is pleased to grant you a non-exclusive limited license to use the Services, including accessing and viewing the Content on a streaming-only basis through the Video Player, for personal, non-commercial purposes as set forth in these Terms.
Although classroom use would be non-commercial, it would not be deigned personal use. Hulu could theoretically cancel your account for a violation.
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 [...] 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.
Although classroom use would be non-commercial, it would not be deigned personal or private use. Amazon could theoretically cancel your account for a violation.