It has been years now with the Firefox/flash problem, every time there is a update I hope its over, but nobe. Its really a big problem and now I am switching to IE fully. Its a shame it really was a good browser.
I've had two problems with flash on firefox - apart from the fact that adobe is rubbish anyway:
1. On linux I installed gnash, hoping it would be a better open. A mistake: some sites refused to work with it because it does not run the latest fancy bits. I had a real job getting the linux machine to drop gnash and run adobe flash.
2. Again on linux, flash suddenly stopped working on my brother's machine (I suspect due to a faulty update of something allied to either flash or firefox). After a couple of months, him trying things ad hoc, me not having the box here to concentrate on it, we have still not got it working.
All other linux and windows boxes (about ten between us) working fine with firefox/flash. OS's are Linux Mint, Windows 2000, Windows 2003 and Windows XP.
For me, it occasionally happens in FF, but I wouldn't say it was a major issue. Of the Windows-based OS, I have XP, Win 7 and Win 8. Flash in Win 7 is the one that crashes, but, as I said, it's occasional.
On my brother's linux Mint it's a computer fault not the browser. Both firefox and opera fail to open flash files. It's easy to lose sight of that when trying to debug the problem. :(
I seldom watch flash but when I do there has been no real problem - perhaps because so infrequent. I use flash-block for better control and to block flash adverts etc. I watch a lot of BBC programs but download them first with get_iplayer and view them in VLC.
Please note that (my) thread at that posting was about ubuntu 10.04 with a mention that I would update the OS to ubuntu 11 or 12. Instead, I switched to Mint Maya Mate and firefox worked with flash for quite a while before failing about a month ago, when ALL things flash failed across the machine, with the exception of get_iplayer which still downloads flash files and converts them (but could never actually play them).
Both have major bugs that are still being found (at least FF is updated when the bug is fixed, not three weeks later!). Apart from that I abhor anything google and chrome is a very suspect privacy hole - at least in my view.
If you are sure you have the latest version of Flash you might be able to stop the crash issues if you don't allow all sites access to flash. Yes, sometimes you'll see an icon instead of an ad, but unless you are trying to view a video you don't need to have Flash enabled. My FF never has crashed.
I don't pretend to think that what works for me works for everyone across all platforms but I would try to see if you can't disable Flash until you click to allow. Windows should offer a way for you to set preferences for Adobe Flash and under "Storage" I see choices (on Mac) that let me choose to allow sites to save information on my computer 3 ways: Never, Always or Ask Every Time. I set it to ask every time.
In FF I get a bar across the top of a page that wants to use Flash and if I don't want it on, I just close the bar. If I want to allow I can "Allow Now" or "Allow and Remember". I'm pretty sure they wouldn't deny Windows users the same choices.
Have you checked to see if you have any corrupted adobe LSOs? (Persistent Flash Cookies) Also in adobe flash prefs don't allow the 10k data it wants to install. Back around 17 or 18 I had a few (and I mean something like 4 o 5) flash crashes. Installed BetterPrivacy for FF to autodelete LSOs at browser close and that pretty much stopped the crashes... then about ver 23 it happened again and that's when I checked the adobe prefs and told it NO to writing anything to my drive. Haven't have a flash crash since... and I do a LOT of flash.
Edit... what not3easy said about prefs... I just remember doing it, not the options. :) BUT the LSOs are a real problem and they are NOT in your cookie folder and I'm not sure where they might be written on a linix install.
I run several firefox windows (currently 8), all with several tabs (average about 8 per window) and have done for years. Can't remember when ff last crashed - I don't think it ever has under linux. And very seldom on an old Windows 2000 machine.
It's worth bearing in mind that Flash is on the decline anyway. Newer web sites are (supposed to be) using HTML-5 which does not require it and many mobile devices do not accept Flash.
At the start of installing a new Windows 2012 web server a few weeks ago I was forced to use IE to get firefox. I hated it!
On a lighter note, Firefox just came close to giving me heart failure. I clicked to upgrade-- I musta blinked, because I swear I installed 26 last week and now it's on 29 --and it told me the download would take about two and a half hours.
Then it recalculated and offered me two minutes and eighteen seconds instead.
Now, would anyone care to hazard a guess how or why 15pt Palatino has chosen to display itself as 13pt-- and, adding insult to injury, to claim it is obeying the site's CSS when doing so?
I used to have that issue with flash crashing, but it hasn't been so prevalent of late. I'm not sure why as it just seemed to stop. It must have been an upgrade or two ago. I'd forgotten all about it crashing.