Northern Districts ended day two on 81 without loss before putting the foot down in the first session of day three.
Flynn in particular took a major toll on the Canterbury attack, bringing up his century in 140 deliveries.
Once reaching triple figures, Flynn savaged Canterbury and reached his 150 just 32 balls later.
Meanwhile Cooper was playing a determined innings at the other end. He reached his half-century off 98 balls and, like Flynn, upped the ante after reaching a landmark.
Cooper hit 11 boundaries and a pair of sixes before a superb front foot cut brought up his second first-class century, much to the delight of the smattering of local support.
He carried on where he left off at lunch after Flynn's dismissal on 157.
He added another five boundaries before hitting a pull shot straight to Michael Pollard on 136.
Cooper was at the crease for 266 minutes.
Canterbury were working their way back into the contest late on the first day.
Canterbury were dismissed for 193 thanks to a five-wicket haul from James Baker before Northern Districts declared on 409 for 4.
Canterbury were on 125 for 2 late on day three after Chad Bowes hit 93.
