Short answer: NO
Except: Netflix Original documentaries with a GRANT OF PERMISSION FOR EDUCATIONAL SCREENINGS - keep scrolling for that list. This is not available for all Netflix Originals and/or Documentaries.
Long answer: The Netflix End User License Agreement or Terms of Use, 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 Alexander Street Press, Swank, Films on Demand, Docuseek2, or Ambrose Digital Video.
The following titles are currently available for a one-time educational screening. Title availability is subject to change per Netflix. 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.
13th - readily available to view on Netflix Youtube
High on the Hog: How African American Cuisine Transformed America