How come flash player won't work in my Microsoft Edge browser?

First, confirm that ActiveX Filtering is configured to allow Flash content:

https://forums.adobe.com/thread/867968

Internet Explorer 11 and Edge introduce a number of changes both to how the browser identifies itself to remote web servers, and to how it processes JavaScript intended to target behaviors specific to Internet Explorer. Unfortunately, this means that content on some sites will be broken until the content provider changes their site to conform to the new development approach required by modern versions of IE.

You can try to work around these issues by using Compatibility View:

http://windows.microsoft.com/en-us/internet-explorer/use-compatibility-view#ie=ie-11

If that is too inconvenient, using Google Chrome may be a preferable alternative.