Having flash die for websites (like small restaurant sites) has mostly already happened and is a good thing.
Having flash die for games would be a bad thing. There are hundreds of thousands of games on the web that are written in Flash that are a lot of fun for millions of folks to play. Just because you can't play them on your mobile device is no reason for the rest of us to lose access to them on our PCs. And, no, most of them will not be converted to HTML5 because they were written years ago and the author has long since moved on.
http://www.homestarrunner.com/flashisdead.html
(requires flash)
Use a virtual machine with windows xp and actual flash for that just like one uses DosBox.
Lots of people bought these when they where up-to date and most aren't interested anymore. You can get these for free from plenty of people.
The fact that windows xp needs to be activated in contrast to dos makes it bit more tricky, but cracks are aviable and legal 1) if you do indeed own a licence.
1) As for every legal discussion on the internet: Different places have different laws. However, I don't think MS cares about XP at this point. In contrast to DOS they don't sell it anymore.
There are just as many (if not more) games for DOS, yet rarely does one lament the death of DOS on home computers, particularly because such games can be run in an emulated environment. That will likely be the case for Flash games someday if they really are all that great (hint: of those hundreds of thousands, a solid 95% are - put as nicely and generously as possible - absolute rubbish).
This isn't to mention that it would be only a matter of time before someone goes about reimplementing with HTML5, original author or otherwise, if the game really is worth that sort of effort.
That difference is also less meaningful with companies like GoG reselling older games, often with the necessary emulation layers for them to run on newer Windows versions (and - lately - Linux). Thus, even some very neglected DOS games are still in distribution. Hell, Super 3D Noah's Ark of all things is on Steam. Super 3D Bloody Noah's Ark. If that manages to be the case, then I'm pretty sure Flash gamers have nothing to worry about in the long run.
That's a compelling reason for me to want flash support everywhere, even if Flash itself dies.