Flash is dead but still working on my colleague's PC , not on mine?

There are industry standard approaches to maintaining legacy software for archival purposes using virtualization and external security to allow users to run unmaintained software safely.  Those solutions are generally not free (from labor or licensing costs), and require a degree of expertise.  Advising on those topics is beyond the scope of what we're going to do here, but you're thinking along those general lines.

Here's the original announcement from 2017 with background and links to the browsers roadmaps: 

https://theblog.adobe.com/adobe-flash-update/

Flash Player is EOL, and all of the major browser vendors will follow pretty soon with updates that remove support for all browser plug-ins.  This means that even with an old Flash Player installed, you'll be hard-pressed to find a browser that will run it.  More importantly, those configurations would not be safe for browsing the open web. 

You have a number of options at your disposal, but the best option would be to update your application to remove the dependency on Flash Player. 

See the enterprise FAQ for your options: 

https://www.adobe.com/products/flashplayer/enterprise-end-of-life.html

The Enterprise Enablement section in the Flash Player admin guide may also be helpful:

https://theblog.adobe.com/adobe-flash-update/