Short answer: NO
Except: The titles to the right are all Netflix Original documentaries which do grant permission for classroom use.
Long answer: The Netflix End User License Agreement, which you agreed to when you created an account, specifies that the account is "only for your personal, non-commercial use." Netflix is not alone here; Amazon Prime, Hulu, and other personal streaming vendors do not grant rights for institutional or educational use.
This is important because licenses overrule copyright exemptions. Showing your personal DVD during class is covered by a specific copyright exemption (Section 110), and showing clips can be covered by fair use (Section 107). However, streaming videos from personal subscription vendors in your classroom when the license prohibits such viewings? There is no copyright exemption for that and the situation is problematic.
This is why the library offers to obtain streaming videos through institutional subscription vendors like Swank, Films on Demand, or Kanopy.
Netflix and Educational Screening (taken from their website):
Some Original educational documentaries are available for one-time educational screenings. To find out which titles are available for educational screenings, go to the "Only On Netflix" section of media.netflix.com. From here, navigate to "All Alphabetical." Titles that are available for educational screenings will display the following grant of permission on their details page:
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 of any of the documentaries noted with this information, on the following terms:
The documentary may only be accessed via the Netflix service, by a Netflix account holder. We don't sell DVDs, nor can we provide other ways for you to exhibit the film.
The screening must be non-profit and non-commercial. That means you can’t charge admission, or solicit donations, or accept advertising or commercial sponsorships in connection with the screening.
Please don’t use Netflix’s logos in any promotion for the screening, or do anything else that indicates that the screening is “official” or endorsed by Netflix.
We trust our users to respect these guidelines, which are intended to help you share and discuss our documentary content in your community.
As of 9/26//2018 the following titles are available for a one-time educational screening. You must have a personal Netflix account in order to show these titles. Always double check the details page for each title, before showing in the classroom, to ensure that the Grant of Permission is still applicable.