I have the same flash file uploaded to two servers. It seems to work perfectly fine on one (IE, Firefox and Chrome) but on the other it works only on Firefox, not even chrome.
The thing is I guess the flash file does load, but until I right click and click play, the file does not start playing.
Could this have anything to do with the server (yahoo small business)
Whether or not a flash file autoplays depends on the HTML code used to embed it - specifically the play parameter (full info here). So the difference you're seeing is not the two servers, but two slightly different HTML pages.
With that said, however, the "play" parameter is only a default behavior - like a suggestion. If you put a play() command in the first frame of the Flash content, then whatever is in the HTML will be ignored, and your SWF will start out playing regardless of how it gets embedded.