I've always got the impression he's an England or noone player. This is from an article in 2020 about him:
Most notably, he helped the Young Lions win the Toulon Tournament in 2017, where he finished joint-top scorer with four goals.
Two of them came in a win against Scotland, who Barnes qualifies for through his maternal grandparents. Paul (his Dad) reveals the SFA's performance director, Malky Mackay, asked 'quite a few times' if he'd be willing to play for Scotland but Barnes is England through and through.