Why yes i have. I'm glad you posted your problem because i almost forgot about this post.
I don't know what method you are using for your popups, the method i was using was some script i found that didn't work that great, and showed hidden div's embedded in the document. I found another solution that works ten times better, its called thickbox. Its based on jQuery and instead of popping up a hidden div, it displays content from a popup iFrame. Since an iFrame is just like another browser window, everything and anything should render correctly.
I have just one flash video embedded in one of my popups and it works great. check out the link above and click on the Celara Denture Technique. You can click on any popup and see that it doesn't look like an iFrame at all, its just styled with CSS.
check out http://jquery.com/demo/thickbox/. This page will give you all you need to implement it.