Flashpoint Archive now has around 200K flash games that can be downloaded and ran locally. Im sure this is nothing compared to what used to exist but basically anything of note is in there
What do you use to run them locally? FLASH doesn't exist anymore and all the emulators do not properly work. I've got an archive of FLASH games myself, but I cannot play them anymore.
Flash Player in the browser doesn't exist anymore. There's still the standalone Flash Player that game with Adobe Flash/Animate, and it works fine. It doesn't depend on browser compatibility, since it runs on its own.
Not a thing on Linux as far as I know, unfortunately.