I have never had any problems with Flash Player myself.
But I’ve heard lots of complaints about 0-day vulnerabilities, etc. Of course, no support for mobile browser. Browser don’t want to support plug-ins. Flash Player is not open source.
Anyway, I’m keeping Flash version of my games on the website as they are still working for me and some diehard players don’t want to switch to HTML5 version.
Moreover I still play some of the games from time to time, like Resistance Is Useless and Mad Tanks.