Any reason for Flash not to work on touch based devices must be not also be applicable to other environments, like HTML5 or native, nor can such reasons be valid if they also apply to different kinds of hardware, for example desktop computers.
I don't have a tablet, nor access to one, so I hadn't thought of the swiping feature that was mentioned in another comment in this thread, which is one such reason. Flash's jail-like environment precludes cross-boundary swiping. Swiping is a feature that's almost unique to touch-based devices. Mouse gestures come close, but I don't believe they're widely used. The problems with it are also unique to browser plugins like Flash, because it does not exist in HTML5-based applications, nor native ones.
I'm having a hard time accepting that is the only reason, though. Is swiping really that important that it and it alone is enough to doom Flash and browser plugins in general?
Then we get to html5. This is a part of the browser. The browser can suspend execution, ensure gestures work before the program responds or any other kind of integration.
As for mouse vs touch screen, I would find a flash site designed for a mouse quite annoying to use with a touch screen. Mouse environments are designed with elements close together, so you don't need to drag your mouse far. You can also use 'hover' effects, where your mouse hovers over an element. This is opposed to a touch screen, where I can easily move my hand/finger across the screen and can't 'hover' over elements. A touch screen also requires bigger hit targets, as you have less accuracy than a mouse.