According to his Twitter, there was only one appointed AR, there wasn't another available so a coach filled in. He posts the league rules stating that the home team must provide flags. This seems incredible for a decent standard league like that one, and they be better off removing it from their competition rules as all refs carry flags.
But once it's been established that the club hasn't got any flags to provide (I can't think of any ref a that would ask for them anyway) just use your own or the other officials flags. Common sense, spirit of the game etc. In law he's right due to competition rules but why would you refuse to use your flags? The answer is of course because he wants to use it to raise his radical referee profile, but in reality he just looks petty.
Whenever he was asked about why he didn't use his own flags he just changes the subject to not being a follower and a load of other nonsense.