@Nick,
Security is a complicated subject and there are all kinds of ways our computers can get compromised. Same as Flash, modern browsers have their fair share of vulnerabilities. See e.g. these recent news. I don't think that Flash is inherently less or more secure than HTML5/JavaScript in our browsers. It is true that Adobe did somewhat poor job at maintaining Flash, including the security issues. They didn't put enough money/effort into it and allowed it to die.
Adobe open-sourcing Flash wouldn't necessarily mean a multitude of variants (forks). Open-source developers are well aware of pitfalls of forking, and most projects exist in only one variant. There are some cases when due to various reasons (personal or technical) there exist two (rarely more) versions of open-source software, e.g. OpenOffice and LibreOffice. There had been cases where projects had split and then, years later, merged back together.
The most relevant to our current topic would be FireFox, earlier Mozilla, earlier Netscape Communicator. It's an open-source browser and there's one main version of it, although there are multiple browsers "based on FireFox". These are all more or less niche browsers with a small user base, so their developers naturally aim for compatibility with FireFox in terms of being able to render all the same websites correctly.
Naturally web developers only test their websites and web applications on the most common browsers. E.g. the company I work for cares for these desktop browsers: Chrome, FireFox, Edge, Safari. We still support IE11 although the percentage of people who use is going down fast. We don't develop or test for any of the niche browsers. Too much work as it is, with all the browsers I mentioned!
Which is why Flash was easier to work with. For the most part it was: write once, works everywhere. In the several years I worked with Flash, I recall only one obscure bug in our application that caused IE to freeze while in FireFox it seemed to work ok. Turned out on IE a "load complete" event listener was fired immediately (synchronously) when loading a file, and asynchronously on Firefox. Our code assumed that every load is async (not the best idea). If there were many files to be loaded in a row, we had a call stack overflow on IE, which was for some reason just freezing the browser, instead of showing an error dialog.
Anyway, I think if Flash was open-sourced and given to the community, there would be a single organization taking care of it, and open-source contributors aiming for their contributions to end up back in that single "standard" Flash Player, rather than making their incompatible forks. We can only guess now, although in some alternate universe this might have happened