Well, if you've exhaustively troubleshot this thing and the conclusion is that none of your browsers work right, that's problematic. Firefox isn't a surprise, but IE (which has been tested extensively by both Adobe and Microsoft and is optimized for the platform), and Chrome (which is also tested extensively both Adobe and Google and we know generally works well on that config) usually work pretty well.
Is this a clean install of Win8.1 on new hardware, or did you do an upgrade install from an older Windows OS? A clean install is always going to give you better results, but I have no actual diagnosis which I could justify as a reason to tell you to reinstall.
If it's an older disk, have you checked the disk for errors recently? It may be something as simple as read/writes are failing at inopportune times and causing the browsers to crash.
Is there a consistently reproducible set of actions that cause the browsers to crash, and is it obvious that it's Flash, or is the whole browser just going down?
You *could* report the crashes to Chrome by going to chrome://crashes and filing bugs. That's the best way to get traction there. If you give me the resulting bug numbers, I can ask the Chrome guys if they have any feedback when I talk to them this week.
An update: My computer has apparently been infected with Adware, but it didn't start showing symptoms till yesterday. I fully resolved the adware issue today and flash started working correctly. I don't know if it's related or just dumb luck, but I am able to use flash with no problems now.
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