You can definitely add a Flash banner to your site, but not in the banner position of a style that has a changeable banner. This is because the banner area does not support .swf files.
You can, however, choose a style that does not have a banner image area and place a Flash Widget at the top of the page and into that your Flash file. You can use a style called "Skyline" which includes the option to remove your banner area. Here's the steps for this:
Once you've selected your style, here's how to add a Flash file to your page: