Is it permissible for my son to play the flute at school parties, knowing that it is not his profession, that he has a talent for playing by ear, and that I consider it forbidden?

This act is Islamically forbidden, and it is not permissible to practice it for a livelihood, because it misleads people and distracts them from obeying Allah. Whoever performs this act is more sinful than those who listen to it. Parents should guide their children to what benefits them and prevent them from this forbidden matter, and encourage them to develop their talents in permissible affairs.