1. Video and animation. We have native browser video tags.
2. Brochureware (static pages, like restaurant websites). Looking back, I think this was done to work around the fact that browsers didn't render things the same. We have much better CSS standards and implementations today.
3. Games. Javascript is much faster today, and there's WebGL.
I never was a big chat user, but WebRTC and sockets seem to cover those uses, too.
Unless I'm missing a whole bunch of things, there's not much reason to keep Flash around on the open web. The security issues alone make it quite a headache.
One is an, um, adult site. The other is HBO Go, which I only know because I had issues getting this running on Linux. I haven't tried it in several months though so that may have changed.
There are a lot of technologies that can be used for chat. Literally by looking for a flash chat room (searched "flash chat room for a website") the third result I got in google was a html5 based one. Just to name a few random examples of open source html/css/js based chats: https://github.com/credija/opa https://conversejs.org/ https://rocket.chat/ https://firechat.firebaseapp.com/ https://deadsimplechat.com/ and since I mentioned css, I have to add this: https://github.com/kkuchta/css-only-chat :)
I’d rather an open source standard exist than a proprietary one.