He was born circa 1913 in Savannah, Georgia and attended Savannah High School. In 1931, Hennemier enrolled at Duke University where he studied business administration and was a member of the Sigma Alpha Epsilon fraternity. He played college football for the Blue Devils under head coach Wallace Wade. Hennemier played as a center and guard, and he was a member of the varsity team from 1933 to 1935. As a senior in 1935, he was named the team's most valuable player. In 1935, he was named to the All-Southern Conference third team. At his heaviest, Hennemier weighed between 150 and 155 pounds, but because of his aggressiveness despite his small size, he was nicknamed "Scrappy Jack". He graduated with the Class of 1936.