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Most of it stems from the client having their screen setting set goofy...........in order to view a site in just about any panel/monitor properly is to have the panel/monitor settings set to normal 96DPI.
We can set a web page to view at 800x600 and then set a 13inch monitor and a 17inch panel to view the same page at the settings of 96DPI (normal) and they both both view incredibly well, it works this way in reverse as well.
Anyway unless you're using resolution-specific images in your Flash, the whole idea of vectored art is that it is scalable and resolution -independent. Using Javascript to detect screen width, you can simply output a table at an appropriate width and scale the flash object accordingly.
Another method is to make it user-configurable. Have a User Options area in which they can select screen resolution, text only, flash/noflash, etc. Store it in a database or something and set a persistent cookie to ID the visitor. Now you can output a lowest-common-denominator size (as in 680px wide or so) unless a cookie is found that tells you to do otherwise.
(IMO both Flash and dependence on Javascript for content present accessability and compatibility challenges to your visitors, but that's not the question on the table. The **best** method is to design problems OUT of your layout and use the width of the screen, whatever that may be, for most applications.)