Parkinson earned four varsity letters as a member of the Kentucky men's basketball team in the Southeastern Conference . He played for Rupp from 1943–44 through 1945–46 and again in 1947–48; during what would have been his true senior season, Parkinson was overseas for 11 months after enlisting in the Army. As a freshman in 1943–44, he helped lead the Wildcats to a 19–2 overall record and win both the SEC regular season and tournament championships. He was named to the All-SEC First Team and All-SEC Tournament Team. In 1944–45, the Wildcats once again were SEC regular season and tournament champions. Parkinson earned his second All-SEC First Team and All-Tournament Team honors while helping the team earn a berth in the NCAA Tournament. They finished the season with a 22–4 record. Parkinson's best collegiate season came as a junior in 1945–46. He averaged 11.3 points per game, earned his third consecutive All-SEC First Team and All-SEC Tournament Team selections while leading the Wildcats to yet more championships, and ultimately led them to win their first-ever NIT. They finished the season 30–2 and edged Rhode Island, 46–45, in the NIT championship game. Parkinson was named a consensus Second Team All-American as well. After the school year ended, he spent an 11-month stint in the Army, which put off his college career by one season. When Parkinson returned in 1947–48 for his senior season, he found himself relegated to coming off of the bench rather than starting, something which he had done for his whole career. He was playing behind what came to be known as Kentucky's "Fab Five" of Alex Groza, Ralph Beard, Cliff Barker, Kenny Rollins and Wallace "Wah Wah" Jones, which is one of Kentucky's most famous all-time teams. Kentucky would go on to win the SEC regular season and tournament as well as the 1948 NCAA Championship, but Parkinson's role in the success was greatly reduced from two years prior. Despite this, he would end his career with a distinguished collection of championships and accolades, including:
Jack Parkinson was selected in the 1949 BAA Draft by the Washington Capitols. He did not play in the league until, however, as a member of the Indianapolis Olympians. In only four career games, Parkinson scored three points. In addition to his brief NBA career, he also played with the Whiskered Wizards basketball team of St. Augustine, Florida, and with the Toledo Mercurys, who traveled with the Harlem Globetrotters.
Later life
Parkinson returned to Yorktown, Indiana and opened a wholesale plumbing and heating business in Muncie. He was elected into the Delaware County Athletic Hall of Fame and the Indiana Basketball Hall of Fame. His son, Bruce G. Parkinson, was an All-American as a player at Purdue and still holds the school's record for career assists. Bruce led the Boilermakers to the 1974 NIT Championship and was the Captain of the 1975 Pan-Am Gold Medal Men's Basketball Team. Bruce was elected to the Indiana Basketball Hall of Fame in 2004. The Parkinsons are one of a handful of father-son pairs who have been elected to the Indiana Basketball Hall of Fame. His grandson, Austin Parkinson, is the current head coach of the women's basketball team at IUPUI. Austin was an Academic All-Big Ten point guard at Purdue. Jack Parkinson died on May 29, 1997, due to complications from a brain tumor.