I see two solutions to that.
First, you could use GET data.
If you want to see GET data in action, look in your URL bar. It is probably in the form
If you use this in the URL for a Flash, it will create variables in your Flash whose values are Strings.
Or, you could restructure your Flashes so that instead of linking, one loads the other.
You could do this using the loadMovie() function, or by using the MovieClipLoader class. You can check the documentation for these at livedocs.adobe.com.
The views expressed in this post are those of an insane lunatic and do not necessarily represent the views of actionscript.org.