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You could only assure that the application looks the same on any resolution if you make your site at the lowest resolution possible. That way, you are assured that no one will ever see it differently. Obviously, this is not a cool thing to do and I'm quite sure that, that's not what you want. Still, you can get quite good results if your site is full browser ( meaning that the .swf file is streched 100% of the browser with and 100% of the browser height ).
A few examples:
As you will see, the website content will adapt to the browser width and height ( even if you resize the window ); but to assure that the web site does not look bad if the user resolution is extremely small, I decided to limit it's minWidth and minHeight ( so if the user's resolution goes under the "minimum recommended" I add a scrollbar and stop the .swf file from scrolling ).
That's the most you can do if you want to keep the site "good looking" in almost every situation.
With best regards,
Using Flex for application development places you at a very comfortable position with regard to uniformity across various platforms. I would suggest always assigning widths and heights in percentages via MXML. That would ensure cross platform uniformity.