What an intriguing query! Unfortunately, there isn't a straightforward solution to this problem. With Flash, the possibilities are endless and it all depends on how the original developer set things up.
Luckily, the Flash Player has an ExternalInterface method in its native API, allowing any Flash application to communicate with JavaScript. If the developer enabled this feature, you can even create an internal callback function in Flash to respond to JavaScript commands, making bidirectional communication possible.
However, if the developer didn't specifically include this functionality, it's unlikely that it exists in the code for you to easily access.
Depending on the structure of the SWF file, there are a few options available. Firstly, you could try adding the parameter LOOP=TRUE to your embed code (more information available here). This may work if the video is a simple timeline animation or if the frames have been added to the timeline using Flash's built-in animation tools.
If this doesn't resolve the issue, things become more complicated. You could attempt to decompile the .swf file using various Flash decompilers to gain insight into its methods and structure. While not an exact science, this approach typically involves some trial and error.
For example, if during the decompilation process you discover an object named "video" of type "Video", you could create a wrapper .swf file to interface with JavaScript by loading the target SWF inside it. If your goal is simply to loop the video, the video object might have an autorepeat property or something similar.
I realize this response was quite lengthy, but I hope it shed some light on your situation. Feel free to ask any further questions in the comments section!