Damkjer started at
NUGF Viborg where he played from U6 to U10, and later played U11-U12 at
Søndermarken IK before moving to
FK Viborg as a U13 player. Here he worked his way up through the club's youth academy and was already a regular in the club's U-19 team at the age of 16. Damkjer was selected for the
Viborg's first-team squad for the first time as a 16-year-old in October 2023 against
Brøndy, and was also on the bench for another five matches that same season, though without making his debut. Damkjer made his debut for Viborg's first-team squad on 13 December 2024, being substituted onto the pitch in the 39th minute in place of teammate
Mads Søndergaard, in a
Danish Cup match against
Danish 3rd Division club
Brabrand. He later scored in the 57th minute and was named as Man of the Match. His Superliga debut later came against
AGF on 9 March 2025, playing for 65 minutes of the match. On 31 July 2025, Damkjer extended his contract with the club until June 2029. == International career ==