The short answer is no. Netflix does grant permission for a few Netflix Original documentaries for classroom use.
Netflix has created a YouTube playlist of its educational documentaries for instructors to stream in their online classes.
Educational Documentaries | Netflix YouTube Playlist
See details in the box below.
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; Disney +, 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 Kanopy, Films on Demand, Alexander Street Press, and Swank Digital Campus.
Adapted from information from the James E. Tobin Library Libguides by Tabitha Ochtera.