You could make your command remember the type it was called from.
private var msgType:String;
public function execute(message:TestMessage):AsyncToken
{
msgType = message.type;
return service.getResponse(message.requestObject);
}
public function result(data:Object):void
{
//Here i want to find out the response is for message type1 or message type2, that called the service.
if(msgType==TestMessage.Type1)
trace("Type1");
else if(msgType==TestMessage.Type2)
trace("Type2");
else
trace(msgType);
}