[1] He made his professional debut that season with the Rookie Arizona League Cubs, going 2–0 with a 3.48 ERA in nine games (six starts).

He spent 2015 with the Class A-Advanced Myrtle Beach Pelicans where he compiled a 7–5 record with a 3.11 ERA and a 1.24 WHIP in 18 starts.

On July 20, 2016, the Cubs traded Blackburn and Daniel Vogelbach to the Seattle Mariners for Mike Montgomery and Jordan Pries.

[9] Blackburn was called up to the Oakland Athletics to make his major league debut on July 1, 2017, against the Atlanta Braves.

On August 22, Blackburn was struck on the hand by a line drive off the bat of Trey Mancini in the fifth inning during a start in Baltimore.

[13] On February 27, Blackburn was outrighted to the Triple-A Las Vegas Aviators and invited to Spring Training as a non-roster invitee.

On January 11, 2024, Blackburn signed a one-year, $3.45 million contract with the Athletics, avoiding salary arbitration for a second time.

[23] On July 30, 2024, the Athletics traded Blackburn to the New York Mets in exchange for pitcher Kade Morris.

On October 11, Blackburn underwent a cerebrospinal fluid leak repair procedure and was ruled out for 4–5 months.