James soon lost his position, being forced to flee the following year after murdering the Royal Chamberlain. Later, he was pardoned and regained the position. In 1463, he became King James II of Cyprus after ousting the Queen, his half-sister Charlotte who had succeeded their father John II.
Although it was not uncommon for medieval monarchs to put relatives in prominent positions in the church, James' youth seems to be very unusual. Googling has not turned up any other information on very young archbishops or bishops.
The only other 'teen' I've been able to find is Odo of Bayeux, half brother of William the Conqueror. Unfortunately, we don't know his year of birth; estimates range from 1030 to 1035 so he may have been as young as 14 or as old as 19 when his brother William made him bishop in either 1049 or 1050.
Were there any archbishops or bishops, either from the medieval period or later, who are known to have been younger than James when they were appointed? Or is the case of James, and even a possibly older 19-year-old Odo, extremely unusual?