William educated at St Joseph's College, at Dumfries Academy; and at Glasgow University, qualifying M.A. in 1909 and M.B., Ch.B. in 1917. Whilst pursuing his medical studies he became a member of the Rangers Football Club, and afterwards transferred to Celtic, where he obtained considerable prominence in Scottish football, and secured his international cap in the League. Afterwards he had been a member of the Bradford Park Avenue Club, for which he played for several seasons.
He took a commission in the R.A.M.C. at the rank of Lieutenant on 6th September 1917 from the Glasgow University Officer Training Corps, then entered the war in East Africa on 18th October 1917. On 30th August 1918 he was severely wounded. He gained promotion to Captain on 6th September 1918.
William was the son of William Kivlichan of St Columba's, Rotchell Road, Maxwelltown.