the FileReference.browse action could be called only in response to a user action(mouse event or keypress event), so you have to modify your code to gain the user action, for example you can use Alert:
public function receiveTextFromJS(s:String):void {
Alert.show("Browse for files?", "", Alert.OK | Alert.CANCEL, null, onAlert);
}
private function onAlert(event:CloseEvent):void
{
if(event.detail == Alert.OK)
{
var myFileReference:FileReference = new FileReference();
myFileReference.browse();
}
}