We will make use of the onbeforeunload event in javascript. So first of all, you will need to insert the following into index.template.html.

<script language="JavaScript" type="text/javascript">
window.onbeforeunload = function()
{
	var swfApp = ${application};

	return swfApp.onCloseApplication();
}
</script>

The all you need is to add a callback function onCloseApplication in your main application (see codes below).

Demo:
Application Exit Warning (view source enabled)

Source Codes: main application

<?xml version="1.0" encoding="utf-8"?>
<mx:Application
	xmlns:mx="http://www.adobe.com/2006/mxml"
	layout="absolute"
	backgroundColor="#F8F8F8"
	creationComplete="onCreationComplete()">

<mx:Script>
<![CDATA[
	private function onCreationComplete() : void
	{
		if ( ExternalInterface.available )
		{
			ExternalInterface.addCallback( "onCloseApplication",
				function():String
				{
					if ( chkDisplayMessage.selected )
					{
						return txtMsg.text;
					}
					return null;
				} );
		}
	}
]]>
</mx:Script>

	<mx:CheckBox
		id="chkDisplayMessage"
		x="37" y="29"
		label="Display message upon application exit"/>

	<mx:Label x="37" y="59" text="Message:"/>

	<mx:TextInput
		id="txtMsg"
		x="104" y="57"
		text="Please don't close me."/>

	<mx:Label x="37" y="107" color="#666666" text="*Check on the above checkbox, then close/navigate away from the current url."/>
</mx:Application>