He was part of the Grand Slam winning side in 1990. He made his Scotland debut 21 January 1989 against Wales alongside his brother, Iain Milne who was representing his country for the 42nd time as prop. Kenny's final appearance came during the 1995 Rugby World Cup in South Africa against New Zealand. In all he won 39 caps and scored 3 tries. Milne was known for his workrate, durability, hard tackling and courage. He went on one British and Irish Lions tour to New Zealand in 1993 playing in the first test v New Zealand.