It ended up getting this to work. I would check the following.
Make sure the process that SPis running under can write to the Directory where the flash file is stored.
The directory is something like: C:\inetpub\wwwroot\wss\VirtualDirectories\PublicSite\wpresources\FlashImageRotator
I also had to set the Trust to WS_MEDIUM in Web.config
(<trust level="WSS_Medium" originUrl="" />)
Some times it seems the control needs to be "refershed" by editing the web part properties and pushing "OK".
Make sure to connect to the anonymous URL, login, edit the flash rotator web part, push OK button. This has fixed this issue for me in the past.