Microsoft Edge suddenly broken, no video or audio in web conference application

I'm not aware of a widespread issue that matches the symptoms you're describing, and you're correct, Microsoft owns the distribution pipeline for Flash in IE and Edge on Windows 8 and higher.  The standard options for reverting to earlier Flash Player versions don't apply.

If you haven't rebooted since things stopped working, I'd start there.

If that doesn't help, you can try reverting recent updates to Flash and Edge to see whether or not they're the source of the problem.  Be methodical and go one at a time, so that you know definitively which one broke stuff.  This will help us to either find the problem, or communicate the issue to Microsoft, if it's an Edge update and not a Flash update in play.

To do this, go to:

Control Panel > Programs > Programs and Features > View Installed Updates

Sort by installation date, and look at the most recent changes.  Does anything correlate to when the symptoms started?  In particular, look for recent updates to Flash Player or IE/Edge.  IE/Edge updates are frequently bundled as Cumulative Update for Windows, so you may have to examine the provided support links to get details. 

If reverting an update makes the site start to work, some information on how to reproduce the problem would be necessary for us to debug and fix the problem.

If reverting updates that correlate to the timeframe doesn't resolve the issue, then there's something else going on.  There's either a problem with the content provider, necessary network traffic isn't being allowed, something is broken at the OS/Driver/Browser level, etc.  

I'd try disabling hardware acceleration as the next step in that instance:

https://helpx.adobe.com/flash-player/kb/video-playback-issues.html

Once you've finished testing, please definitely re-apply any updates you reverted by running Windows Update and installing the available updates again.

Let us know what you find.