<?xml version="1.0" encoding="utf-8"?>
<s:View xmlns:fx="http://ns.adobe.com/mxml/2009" 
		xmlns:s="library://ns.adobe.com/flex/spark" 
		title="FacebookAuthView"
		backgroundAlpha="0" actionBarVisible="false"
		viewActivate="view1_viewActivateHandler(event)"
		removing="view1_removingHandler(event)"
		creationComplete="view1_creationCompleteHandler(event)">
	<fx:Script>
		<![CDATA[
			import com.facebook.graph.FacebookMobile;
			
			import mx.events.FlexEvent;
			
			import spark.events.ViewNavigatorEvent;
			
			import vo.Profile;
			
			private var thisProfile:Object;
			private var facebookWebView:StageWebView;

			override public function set data(value:Object):void 
			{
				thisProfile = value as Profile;
			}		
			
			override public function createReturnObject():Object
			{
				return thisProfile;
			}			
			
			
			protected function view1_viewActivateHandler(event:ViewNavigatorEvent):void
			{
				facebookWebView = new StageWebView();
				facebookWebView.viewPort = new Rectangle(0,0,stage.width,stage.height);
				var permissions:Array = ["publish_stream"];
				FacebookMobile.login(onLogin,this.stage,permissions,facebookWebView);
			}
			
			private function onLogin(success:Object,fail:Object):void
			{
				thisProfile.facebookConnected = true;
//				navigator.popView();
			}
			
			protected function view1_removingHandler(event:ViewNavigatorEvent):void
			{
				facebookWebView.dispose();
			}
			
			protected function view1_creationCompleteHandler(event:FlexEvent):void
			{
				
				FacebookMobile.init("your dev key here",onLogin);
			}
			
		]]>
	</fx:Script>
	<fx:Declarations>
		<!-- Place non-visual elements (e.g., services, value objects) here -->
	</fx:Declarations>
</s:View>

Using the Facebook AS3 library to authenticate in a Flex Mobile View

Facebook Auth View

ActionScript 3