As a 16-year-old, Zykov played in the MHL with CSKA-Krasnaja Armija Moskva, the junior affiliate for HC CSKA Moscow of the Kontinental Hockey League.

[9] After attending the Kings training camp, Zykov was assigned to begin his rookie professional season in 2015–16 with the Ontario Reign of the AHL.

Zykov compiled 7 goals and 14 points in 43 games with the Reign before he was traded by the Kings along with a conditional 5th round pick (if Los Angeles advanced to the 2016 Western Conference Final, failed) to the Carolina Hurricanes in exchange for Kris Versteeg on 28 February 2016.

As the club's reserve forward, Zykov was a frequent healthy scratch, and was reassigned on a conditioning loan back to the Checkers on 13 November 2018.

As a free agent leading into the 2021–22 season, Zykov returned to his native Russia and agreed to a contract with contending KHL outfit, SKA Saint Petersburg, on 12 October 2021.