The header div usually contains a background image - nothing cheating about that - and supporting text or divs is commonly placed 'on top' of that (inside the header div). If having a background image in a header div were not w3c compliant, rather a lot of us would be up the creek without a stylesheet.
You can't set slideshow - flash or otherwise - as a background image. You would need to create a div within the header image to hold the slideshow.
You'd be best to create what you want for the header as far as possible as one background image - everything you have so far could be one background image (colour, logo, Buckingham) you could then easily create a div for your slide show without worrying about displacing those other divs.
You could certainly create a div in the header for a server-side include, but there wouldn't be much point if it were only appearing on that one page, and wasn't going to be changed often.
Probably the best idea would be to roughly mock up (in photoshop or other graphics software) what it is you want the header to look like so that we can help with the css.
