A subscription to a streaming service, may not cover showing its content in an educational setting. If you are showing videos through your personal streaming subscription you may be violating the terms of use.
Currently, Netflix is the only personal streaming service that allows some of its documentaries to be shown in an educational setting. According to Netflix:

"Some Netflix 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.
Titles that are available for educational screening will display [a grant of permission on their details page]."
Currently, Amazon Prime Video, Disney+, HBO, and Hulu DO NOT grant any rights for institutional or educational use. Licenses overrule copyright exemptions, so this can not be covered under fair use. This is why we offer Swank and Discovery streaming services.
Special thanks to the JET Library Streaming Media LibGuide, UM Flint Media in the Classroom LibGuide and UMich Copyright and Using Video LibGuide for providing clear information on this topic.