Yeah, that's pretty wild. Good times.
The optimal solution would be to license a maintained version of Flash Player from HARMAN. That will give you a copy of Flash Player that your organization can use moving forward, and HARMAN is doing the ongoing maintenance to keep Flash updated with security and functional updates. From an operational headache perspective, it's money well spent.
More details on your options are here, with links to HARMAN's ongoing support offering:
https://www.adobe.com/products/flashplayer/enterprise-end-of-life.html
As a quick and dirty "cross your fingers and hope" solution to get you up and running, you can try this. It's super permissive and may or may not work. If it doesn't, you'll need to do the troubleshooting above to figure out what you actually need to allow, and then make the allow rules accordingly.
Assuming the application is just loading local Flash assets, just make a text file called mms.cfg and put it in C:\Windows\System32\Macromed\Flash and C:\Windows\SysWOW64\Macromed\Flash
It should look like this:
# Enable the AllowList feature (on by default, but here for good measure)
EnableAllowList=1
# Allow Flash Player to match on non-conforming RFC 3986 URIs
EnableInsecureAllowListLocalPathMatching=1
# Allow all local files to load
AllowListUrlPattern=file:*
# Allow children of the parent SWF to load anything
AllowListRootMovieOnly=1
At that point, restart your application. It will either load or it won't.
If it does, great! It's not the best configuration, and you should -- at your leisure -- take the time to understand the implications and decide whether or not more limited rules would be appropriate for your situation.
If not, you (or one of your IT engineers) is going to have to commit an afternoon to learning more about Flash that you ever wanted to. Sorry, sincerely. The instructions above should get you going. If they don't, send me back the actual log output and your mms.cfg, and I'll try and help.
Regardless, you still probably want to talk to HARMAN about licensing the ActiveX Flash Player (and or pressure your equipment OEM to release updated software in the meantime).