His outstanding ability in two sports led to him earning his nickname "Flex.” Flexen initially committed to play college baseball for the Arizona State Sun Devils but was drafted in the 14th round of the 2012 Major League Baseball draft by the New York Mets and was lured away from his commitment by a $375,000 signing bonus.

[1] Flexen spent 2015 with Savannah, the Brooklyn Cyclones, and the GCL Mets, where he posted a combined 2.42 ERA in 12 games between the three clubs.

He also became the fifth Mets player in franchise history to give up a home run to the first batter he faced in the Major Leagues after allowing one to Manuel Margot on only his third pitch.

[6] On August 8, 2017, Flexen recorded his first major league win against the Texas Rangers at Citi Field, pitching 5+1⁄3 innings, allowing three earned runs and striking out four batters.

Among qualified American League pitchers that year, he finished in the top 10 in ERA (3.61), wins (14), ERA+ (111), Fielding Independent Pitching (3.89), and games started (31).

In 2023, Flexen made 17 appearances for Seattle (including 4 starts), and struggled to an 0–4 record and 7.71 ERA with 29 strikeouts in 42 innings pitched.

[19] On July 3, the Mariners traded Flexen and Trevor Gott to the New York Mets in exchange for Zach Muckenhirn.

[22] After two starts for the Triple–A Albuquerque Isotopes, Flexen had his contract selected to Colorado's major league roster on July 29.