You can enable per page skins in Administration> Site Settings and then you can use a different skin on the home page.
You could put the Flash object in the layout.master file of the skin used by your home page.
Note that the skins used by the site are located at /Data/Sites/[SiteID]/skins, for a new installation, SiteID will be 1.
For more info read the skinning documentation
Hope it helps,