What you'll have to do is have 3 divs really. One containing div which will hold the flash and the form. One div for the flash element, positioned (relatively or absolutely) with a z-index of like 1. Then for your form, another div, positioned (relatively or absolutely) with a z-index higher than that of the flash. Usually it's good to make sure it's the top-most item with like 50 or 99 as the z-index.
Now, that should work. I can't guarantee that it will for all browsers as some may just make flash the top-most layer no matter what. But I believe IE 6 and up, Firefox, Safari and Opera all will show the flash under the form.
BTW: I'm moving this to client-side forums.