[6] Upon a first-round elimination from the WHL playoffs, Fleury was signed to an amateur try-out with the Hurricanes' American Hockey League affiliate, the Charlotte Checkers.

On April 12, 2015, in the Checkers final home game, Fleury made his professional debut, scoring a goal, in a 4–3 victory over the Rockford IceHogs.

[13] After the Hurricanes failed to make the post-season, Fleury was assigned to the Checkers to help them in the 2018 Calder Cup playoffs.

[14] The following 2018–19 season, Fleury again made the Hurricanes' opening night roster,[15] but was re-assigned to the Charlotte Checkers on October 17.

[22] On July 21, 2021, Fleury was selected from the Ducks at the 2021 NHL Expansion Draft by the Seattle Kraken, reuniting him with his brother Cale.

[23] As a free agent after the inaugural season with the Kraken, Fleury was signed to a two-year, $1.525 million contract by the Tampa Bay Lightning on July 13, 2022.