Looks like you just need to use a wmode for the Flash. From an old post:
Window Mode (wmode) - What's It For?
There are three window modes.
In windowless modes (like opaque), Flash Player doesn't have a hWnd. This means that the browser tells the Flash Player when and where to draw onto the browser's own rendering surface. The Flash movie is no longer being rendered on a higher level if you will. It's right there in the page with the rest of the page elements. The Flash buffer is simply drawn into whatever rectangle the browser says, with any Flash stage space not occupied by objects receiving the movie's background color.