There are many many different ways to skin every cat, but at the very least you need to make sure your SWF content scales to the container size. If it's a fixed size, all bets are off. The real challenge is getting something in the left column to conform to changes in the right column, especially when using just CSS and DIVs. I'm not sure that's possible without some unnatural and complex gymnastics.
A simpler, more direct, and possible old-school method is to just use a TABLE with a single row and two cells as your column structure. Force the table to fit the page using 100% width and height. Then you're guaranteed that the left column will always be the height of the right column. At that point you just need to make sure the SWF container in the right column uses a % for its height.
Another approach is to use javascript to intercept browser resize events and to resize the SWF container when that happens.