The death of Henry Wardlaw left the bishopric of St Andrews, the most prestigious Scottish see, vacant, and it was James who was postulated to the vacancy.

During the minority of James III, Kennedy took a leading part in political affairs and was frequently able to reconcile contending noblemen.

He was made Chancellor of Scotland in May 1444 after the expulsion of Sir William Crichton, but resigned the office a few weeks later on finding that his duties interfered with his ecclesiastical work.

When the schism in the papacy assumed a very critical character, Kennedy undertook a journey to Rome with the intention of promoting a reconciliation.

In 1450 he founded St Salvator's College in St. Andrews, endowing it liberally with the teinds of four parishes that had formerly belonged to the bishopric.

He also built a large vessel called the "Saint Salvator", which was frequently used by royal personages, and regarded as a marvel, until it was wrecked near Bamburgh while on a voyage to Flanders in 1472.

It is stated by Bishop Lesley that Kennedy's college, ship, and monument each cost an exceptional amount of money.

Bishop Kennedy is a significant character in Black Douglas by Nigel Tranter, where he is depicted rather unfavourably.