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If you are doing fullscreen, you need to set your stageScaleMode to NO_SCALE, and embed your flash object into a div that has its height and width parameters set to 100%. To deal with resizing, your flash project needs a resize event listener (applied to the stage), and all display objects need to respond to that resize listener. Once your swf is resizing properly, you can, as already noted, use stage.stageHeight / stageWidth to retrieve exact dimensions internally.
You're correct in the initial piece of the sequence - sending flashvars in on load, but to respond to screen size changes, you will need to apply one of these techniques.