While there have been no clear legal judgments on the permissibility under copyright law of streaming films from course websites, these steps will strengthen your case for fair use:
Netflix makes a selected number of original documentaries available for one-time educational screenings. To find out which titles are available for educational screenings, go to the "All Alphabetical" section of Netflix Originals and look at the full entry for the film you are interested in. If the film is available for educational screening, the Grant of Permission for Educational Screenings will be right on the listing (see Audrie & Daisy for an example). Permission to screen the film for educational use stipulates that the film must be accessed via the Netflix service, and may be done one time only.* Because the one-time educational screenings are just that, one-time, there is no way to make the film available on demand.
*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