[citation needed] McKenna played his college hockey for St. Lawrence University, an NCAA Division I team in the ECAC.

[citation needed] For a third consecutive season, McKenna continued his journeyman career and signed a one-year, two-way contract with the Columbus Blue Jackets on July 5, 2013.

[5] He started the season in their AHL affiliate the Springfield Falcons but was recalled by the Blue Jackets on December 3, 2013, after Sergei Bobrovsky went down with an injury.

On December 12, 2013, McKenna made his Blue Jackets debut in relief of an injured Curtis McElhinney, saving 17 of 18 shots faced in a 4–2 win against the New York Rangers.

In the 2014–15 season, after the trading away of Arizona goaltender Devan Dubnyk, McKenna was recalled to the NHL again where he started one game for the Coyotes.

With the Coyotes changing AHL affiliates to Springfield, MA, McKenna was signed to a one-year, two-way contract with the new Portland Pirates' parent club, the Florida Panthers, on July 1, 2015.

On March 1, 2017, he returned to the Tampa Bay Lightning organization after he was traded by the Panthers in exchange for fellow goaltender Adam Wilcox.

[citation needed] As a free agent in the off-season, McKenna extended his career in agreeing to a one-year, two-way contract with the Ottawa Senators on July 1, 2018.

He appeared in 10 games with the Senators, posting 1-4-1 record before he was traded along with Tom Pyatt and a 2019 sixth round draft pick to the Vancouver Canucks in exchange for Anders Nilsson and Darren Archibald on January 2, 2019.

[13] He was waived after backing up Jacob Markström for two games, with the Canucks' intention being to reassign him to their AHL affiliate, the Utica Comets.

He was promptly claimed on waivers by the Philadelphia Flyers as they dealt with injuries to goaltenders Brian Elliott, Michal Neuvirth, and Anthony Stolarz.