I do not have a specific answer (i.e. code) for you, just want to get your feedback on this analysis... and a warning... this will get technical...
Seems you have 3 instances of Flash. Each opens its own audio progressive stream, and are essentially independent of each other. Because you're using iWeb, it's not easy to modify code because iWeb itself generates the Javascript and other code each time you add the widget, and that code is spaghetti, usually uncommented and tough to edit.
Plan "A"
Thus, it might be easier to simply find another Flash widget which is a single player that allows multiple audio files to be called (usually within an external XML file) selected by the user. Doing so will change the design, most likely, because selection of the audio file might be in a pulldown menu or similar. The better Flash software allows you to assign individual ID's so you can list and link each audio selection in your HTML, but it ties into the same player.
I know your next question is, do I know of any such Flash audio player which you can use and maintain your existing layout? Answer: No, but now you know what to ask for here on the forum!
Plan "B"
If you want to edit the widget code via iWeb (brave soul) and use the existing Flash and preserve the layout you got now, my advice is to work with Javascript which actually interfaces quite well with Flash.
First, visit this page and read it very, very carefully, over and over if necessary, to get the full impact of it:
http://www.permadi.com/tutorial/flashjscommand/
That excellent page is a simple approach to controlling Flash, i.e. you can make it stop playing by referencing an ID added to the object tag and two other tags added to the embed tag for your Flash. Now each instance of the player can be uniquely identified. At this point you can write Javascript code using the help on the page I linked to ensure the other players, if running, are stopped, when one is selected using the Play() and StopPlay() functions, etc. You'll notice you can also use setVariable() and getVariable() to communicate with your Flash, i.e. to check to see if a variable is set if its playing, if your Flash supports that. And this page is just the simple stuff, see the link on the bottom for more functions.
Example:
You write a function called via onClick when the play button is pressed on one of the Flash objects, it will call a Javascript function you write which might, for example, simply send commands to stop the other two based on the ID passed to that function. That's the easy part, the hard part is integrating this into iWeb horrible code, and my advice is DON'T spend too much time on plan B.
-jim