Definitely Connaught Rangers - the shoulder title is CONN.RANGERS, and the formation patch looks like that of 16th (Irish) Division, which would put him in 6th Battalion Connaught Rangers in 47th Brigade.
Adrian
EDIT: P.S. Was your man born in Moira, Co.Down, c.August 1897, son of John?
If so, then his service record is on Ancestry (indexed as Patrick Flanigan, service no.6624) and there are 2 medal/SWB cards - one with each spelling.
He joined 4th Bn (a training battalion) in Oct 1916, then posted to 6th Bn in France Jan 1917, serving with them until discharged in Jan 1919.