Hlynsson was born on January 23, 2004 in Odense, Denmark. The Icelandic youth international joined Ajax from Icelandic club Breidablik in January 2020. On December 15, 2021, he made his debut in for the first team during the TOTO KNVB Cup match between Ajax – BVV Barendrecht: 4-0. The right-footed midfielder has played twice for the Ajax first team and managed to score once on both occasions.
In addition, Hlynsson played 21 matches for Jong Ajax in recent seasons