Originally undrafted by teams in the National Hockey League (NHL), Kinkaid has previously played for the New Jersey Devils, Montreal Canadiens, New York Rangers, Boston Bruins, and Colorado Avalanche.

[7] In the final stages of the 2012–13 season, Kinkaid was recalled from Albany, and made his NHL debut in a relief role with New Jersey on March 5, 2013, against the Tampa Bay Lightning at the Prudential Center.

[11] Acquired for added insurance to the Blue Jackets' Sergei Bobrovsky and Joonas Korpisalo, Kinkaid remained on the roster as the third choice goaltender and did not make an appearance with Columbus.

As a free agent from the Blue Jackets, Kinkaid was signed to a one-year, $1.75 million contract with the Montreal Canadiens on July 1, 2019.

On February 29, 2020, Kinkaid was reassigned on loan by the Canadiens to the Charlotte Checkers of the AHL, the primary affiliate of the Carolina Hurricanes.

[14] Kinkaid left the Canadiens organization after his lone season with the club, and was signed as a free agent to a two-year, $1.65 million contract with the New York Rangers on October 9, 2020.

Acquired to add positional depth to the Avalanche organization, Kinkaid was immediately assigned to AHL affiliate, the Colorado Eagles.

[20] Before he featured with the Eagles, Kinkaid was promptly recalled to the Avalanche and made his lone appearance in relief of Alexander Georgiev in a 7–3 defeat to the Dallas Stars on March 4, 2023.

As a free agent Kinkaid left the Avalanche and opted to sign a one-year contract with the lone AHL independent club, the Chicago Wolves, on July 18, 2023.

[22] Before playing a game for Chicago, however, Kinkaid signed a one-year, two-way contract to return to the New Jersey Devils on September 13.