FlashPlayer being discontinued? How can we run enterprise FlashBuilder apps on IE?

Back in 2017, Adobe, in collaboration with the major browser vendors in the US, announced a roadmap for deprecating browser support for Flash Player at the end of 2020.  We're still on-track for that timeline.

See the announcement below for details:

Flash & The Future of Interactive Content | Adobe Blog

Preserving the functionality of legacy applications in Enterprise environments while addressing the security limitations of those legacy technologies isn't a new problem, and there are a host of virtualization technologies that your organization might choose to employ while transitioning to modern solutions.

Determining what technologies or solutions are appropriate and best-suited to your organizational and compliance needs is an undertaking in and of itself, and regardless of the solution you choose, it's unlikely to be free in terms of either cost or effort.

Our goal in providing three years of advanced notice, was to give you ample time to evaluate your options and perform the work necessary to make that transition.

If it were me, I'd probably be looking at a virtualization solution where I provided a captive environment where users on modern operating systems accessed a dedicated virtual host, which maintained an instance of an ephemeral copy of a pristine, known-good legacy configuration that included an OS, Browser and Flash combination that works for your enterprise application.  I would also be thinking along the lines that the environment was restricted such that the only things it could access are trusted intranet applications.  This way you've mitigated the risk of accessing untrusted content from a stale, unpatched Flash, OS and Browser combination, and by keeping those instances ephemeral and isolated from the larger network environment, minimized the risk of a compromised host persisting or pivoting to other systems in your environment.

Citrix and VMWare might be good vendors to look at for that kind of a solution, but you'll really need to dig into the specifics of licensing costs, convenience and productivity impact and the risks, costs and timelines involved with simply migrating to an HTML and JavaScript solution as part of that consideration.

Flex was deprecated and transitioned to the Apache project several years ago, where it's actively maintained.  I know that there are libraries for compiling your Flex project to native HTML and JavaScript, which might also be appropriate and worthy of consideration.

The short answer is that there's no magic bullet or one-size-fits-all solution.  Flash is going away, and you'll need to find and execute the transition strategy that works best for your organization.