I use Fedora - two monitors work fine. Yes, at the very start (a few seconds after the start of the gnome), the background image is slightly offset, but it normalizes itself. As far as I know (at one time I was digging a lot on this topic) - there is a problem with two monitors in Fedor, if two video cards are used. Other distributions also exist, but a little less. If you use one video card with two outputs, everything works quite well.
But the flash player - it does not work properly anywhere. On a poppy machine (also with two monitors), if you expand to full screen on another monitor, the dock on the main monitor disappears. As soon as you exit with fullscreen - the dock appears.
On my computer, the flash player sometimes turns on the floor of the screen (that is, it feels like it is trying to place a picture between the screens, but does not draw half). And it is unlikely to greatly depend on the distribution. If the flash player is a YouTube view, then switch to html5 mode - this player works noticeably better for me than a flash player, although there are glitches. But it works exactly in full screen mode (in Google Chrome).