Comment on WordPress Header Images by SEO Dave.
You’ve added it as a linked image (looks like you uploaded the swf file via the WordPress media uploader and inserted it as an image) to a text widget, swf files aren’t images they can’t be added that way, the code has to be embedded correctly.
Do a Google search for “Embedding an SWF File” and there will be loads of examples.
There’s no built in SWF file support in Stallion, no idea if WordPress has anything built in as I’ve never used an SWF file I’ve uploaded. As a side not your swf file works if you load it directly, all you have to do now is build the correct embed code so it works inside an HTML webpage and add it to a text widget instead of adding it as a linked image.