Born in Bansha, County Tipperary, Flannery first began playing rugby with Kilfeacle and District RFC, before going on to attend Rockwell College, where he helped guide the school to the semi-finals of the 2018 Munster Schools Rugby Senior Cup.
He achieved a maximum of 625 points in his leaving cert, which resulted in Flannery being awarded the prestigious Naughton Foundation scholarship, and he is now studying chemical engineering at the University of Limerick.
[1] Flannery made his Munster A debut in their 34–17 win against Dragons A in round 3 of the 2018–19 Celtic Cup on 21 September 2018.
Flannery was a late call up to the bench after Shane Daly was injured during the warm-up and Darren Sweetnam was promoted to the starting XV.
[5] Flannery made his first start for the province in their 31–17 win against Italian side Benetton in round 16 of the 2020–21 Pro14 on 19 March 2021.