Hlynur was a key player with the Icelandic national team when it made its first appearance in EuroBasket in 2015 and again in 2017.

[13] On 23 March 2018 Hlynur was fouled hard by Ryan Taylor in game three of Stjarnan's first round series against ÍR.

[20] On 17 February 2019, Hlynur had 13 points and 14 rebounds in Stjarnan's 84–68 victory against Njarðvík in the Icelandic Cup finals.

[22] On 4 March 2019, Hlynur became the Úrvalsdeild all-time career assists leader, surpassing Guðmundur Bragason.

[23] Stjarnan opened the 2019–20 season with a 89–77 win against reigning champions KR in the annual Icelandic Super Cup where Hlynur posted 12 points and 7 rebounds.

[28] Hlynur was a part of the first Icelandic national basketball team to qualify for a EuroBasket tournament, in 2015.

[33][34] In July 2019, Hlynur agreed to return to the team for its games against Portugal and Switzerland in the EuroBasket 2021 qualification due to injuries in the squad.