In an interview following Jaden Warner's league debut for Norwich against Blackburn, Blackburn's Director of Football Gregg Broughton commented about the success of players from Norwich's recruitment programme in London that Broughton oversaw. He named Kristian Hlynsson as one of them along with Warner, Jon Rowe, Tony Springett, Abu Kamara, Tyrese Omotoye, Saxon Earley, Nelson Khumbeni and Alex Matos. All of whom were in the same age group. The coaching/scouting team was Jay Marshall, Ryan Gordon and Ross Embleton.

Kristian made his professional debut for Breioablik in Iceland before transferring to Ajax in 2020. He played for Jong Ajax before making his full Ajax debut on 19th August 2023 against Excelsior.

He has played for Iceland at Under-15, Under-16, Under-17, Under-19 and Under-21 levels.

His brother is Agust Hylnsson.