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.
GRANT OF PERMISSION FOR EDUCATIONAL SCREENINGS
Netflix is proud to present original documentaries that speak to our users in a meaningful way. We know that many of you are as excited about these films as we are; and because of their informational aspects, you’d like to show them in an educational setting -- e.g., in the classroom, at the next meeting of your community group, with your book club, etc. Consequently, we will permit one-time educational screenings, "one-time screening" means that you can't hold screenings several times in one day or one week - but if, for example, you're an educator who wants to show the film once a semester over multiple semesters, that's okay.
Educational screenings are permitted for any of the documentaries noted with this information, on the following terms:
We trust our users to respect these guidelines, which are intended to help you share and discuss our documentary content in your community.
To the extent your institution requires you to demonstrate that you have a license for your screening, please show them this page.
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.
As a for-profit institution, 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.