These two values in particular can be interesting:

fmt=22: This is an MP4 video in HD quality. On my tests, the resolution can go up to 1280 x 720.

fmt=18: This is a 480 pixels wide version that can be used in portable devices such as iPods.

In order to use this additional parameter, just add an argument to the constructFLVURL method:

// Set "format" to 22 for the high resolution version, or 18 for the iPod one. Or just
// leave to -1 for the low res version.
private function constructFLVURL (video_id:String, t:String, format:Number = -1):String {
  var str:String = "http://www.youtube.com/get_video.php?";
  str += "video_id=" + video_id;
  str += "&t=" + t;
  if (format >= 0) {
    str += "&fmt=" + format;
  }
  return str;
}