What OS and how much RAM do you have? What video card?
Windows 7 64bit 1.73ghz , 8gb ram, Intel Quard core, ATI mobility Radeon HD 560v. System is really fast even editing video and even Photoshop files over a gig. But Flash is killing me lately.
There's only a memory option for exporting when compiling but that isn't really your issue. At home I use my laptop for CS5.5 on an older quad i7 1.6, 4GB ram, radeon mobility HD4xxx series in Win7 64 and it works great (alongside Photoshop, Flash Builder and other misc apps at the same time) so you should be more than fine.
If you also run Photoshop at the same time, do check the RAM default settings. I had some issues because by default it's allowed 50% total RAM. I have half your ram. About ~800MB for the OS, 2GB for Photoshop leaves just over 1GB for "everything else". If you have large PSDs open you could easily eat 4GB ram and not even know Photoshop will do that.
Aside that, the first thing I'd suggest is the usual 2 obligatory options and we'll take it from there. #1, check for updates (Help->Updates) and perform any updates listed. If that doesn't work I'd try resetting your application preferences. To do that (close Flash if it's running), start Flash and immediately after you click the icon to launch Flash hold CTRL+ALT+SHIFT. Delete your prefs and let Flash recreate them. That often fixes odd crashing and performance glitches.
Let me know if those don't help. If they don't it sounds like you're in pagefile territory or your FLA is simply way too big.