When you design your flash work (.fla) you may choose any background color you like. Make sure however that your content/images etc.. etc.. doesnt take up the entire canvas or stage.
Once you export the .fla to a .swf, you take the .swf file and embed/import onto your site. Open the properties manage on the .swf by usually double clicking on it or by right clicking over the .swf and selecting properties.
You can change it size and quality of the .swf but you'll also have the option to select "transparent" bgnd. Checkmark that box. When you prieview your page you can see that regardless of the bgndcolor you selected when creating the .fla file it is now transparent and you can see the actual bgnd images on your site.