I've been grappling with Actionscript (Flash) intregration recently, largely for synchronising the dynamic elements here. In AS2, here's how it's done.

To call a function

Actionscript code

import flash.external.ExternalInterface;

ExternalInterface.addCallback( "methodName", this, method );
function method() {
   trace("called from javascript");
}

Javascript code

function callAS() {
   swf.methodName();
}

To push a variable

Javascript code

function doPassVar(args){
	var sendText = args.value;
	window.document.myFlash.SetVariable("myVar", sendText);
}