[1] He was originally signed by the Boston Red Sox in 1955, and played that season for a lower-level farm team, the Bluefield Blue-Grays, posting a 9.90 ERA in two appearances.

In 1956, he played for a Brooklyn Dodgers farm team, the Shawnee Hawks, where he had a 4.50 ERA in 40 games, including 15 starts.

[2] He then pitched two seasons in the Los Angeles Dodgers' system; 1959 with the Great Falls Electrics and 1960 with the Triple-A Montreal Royals, registering 4.19 and 3.86 ERAs, respectively.

He made his MLB debut on April 15, pitching three innings in relief against the New York Yankees, allowing three hits and one run.

[4] Kunkel finished the 1962 season with Milwaukee's Triple-A affiliate, the Toronto Maple Leafs of the International League, pitching to a 6–1 record with 2.35 ERA in 15 games (two starts) and 46 innings of work.

At the end of spring training in 1965, Kunkel was released by the Atlanta Crackers, the Braves' affiliate in the International League that season.

Kunkel's experience as the plate umpire is documented in the MLB official highlight film of the 1977 All-Star Game.

[19][20] On September 28, 1975, exactly one year later, Kunkel was behind the plate when four Oakland Athletics pitchers—Vida Blue, Glenn Abbott, Paul Lindblad and Rollie Fingers—combined to no-hit the California Angels, 5–0.

[21][22] On September 30, 1980, Kunkel caught pitcher Rick Honeycutt of the Seattle Mariners using a thumb tack to illegally alter baseballs during a game against the Kansas City Royals.

[31] There is a park named in Kunkel's honor in the Leonardo section of Middletown Township, New Jersey,[32] where he had been a longtime resident.