KhanAcademy.org uses YouTube to host their videos. However, they also have these videos hosted elsewhere that are accessed automatically when YouTube is unavailable, such as when it is blocked.
SecureSchool, ISBossBox, LibraryDoor,
To allow KhanAcademy to play videos off of their own servers, as opposed to YouTube's, you simply need to allow a handful of websites.
Repeat this for the following websites as well:
Website Filtering > Website Access > Add A Site
Site IP or Net Address: khanacademy.org
Reason for Change: Allow KhanAcademy
Add Port Access Rules: Check
Commit Changes and Restart Services when finished.