Bairns striker Carl Finnigan drove the visitors into the lead after three minutes only to see Danny Invincibile level five minutes later from a Garry Hay cross.
A good first half deteriorated after the interval but in the 57th minute Flynn's corner from the left evaded a packed six-yard box and made its way in at the far post as the Killie defence stood stunned.
It was an invaluable and deserved win for the Bairns who went within a point of their hosts, who, on this evidence, are in for a tough second half of the season.
The match began in blizzard conditions but the whirlwind opening moments served to warm up both sets of fans.
The visitors adapted quickly to the tricky conditions and raced into a third-minute lead when Finnigan flashed a Scott Arfield pass past Killie keeper Mark Brown from around 14 yards.
However, it took only five minutes for the home side to respond. Hay worked his way into the left-hand side of the Falkirk penalty box and lobbed a cross to the back post where Invincibile's volley went in off the post despite the best effort of Bairns' keeper Robert Olejnik.
In the 15th minute of a remarkably open game Killie striker Mark Burchill dispossessed Falkirk stopper Brian McLean on the left-hand side of the Bairns' box, but fired in an angled drive straight at Olejnik when a cut back to Mehdi Taouil might have brought a better reward.
As the game swung towards the Ayrshire side, Olejnik had to make another point-blank save from Burchill whose mobility was proving a threat to the visiting defence.
What the game lacked in technique - which was quite a lot - was supplemented by pace and raw aggression.
Neither side could take complete control of the match which was adding to the entertainment.
Just after the half-hour mark, though, Finnigan headed a Toufik Zerara cross inches over the bar from eight yards out when he ought to have hit the target.
The game tailed off towards the end of the half but within minutes of the restart Killie midfielder Craig Bryson weaved his way into the Falkirk box where his shot was cleared by Bairns' defender Mark Twaddle.
At the other end, Falkirk playmaker Vitor Lima drove wide of the target from 25 yards to end a brief spell of pressure.
But in the 57th minute the visitors took the lead with an unusual goal.
Flynn decided to take over corner duties from Zerara and his effort from the left evaded a packed six-yard box and made its way over the line in at the far post with the Killie defenders standing in stunned disbelief.
As the home fans instantly turned on their side, they might have found themselves two behind seconds later.
With the Rugby Park defence posted missing, Twaddle set up Pedro Moutinho but the Falkirk striker almost had too much time to tee up his shot before driving just over the bar.
In the 65th minute Killie skipper Kevin Kyle latched onto a Jamie Hamill cross eight yards out but his header was straight at Olejnik.
Killie boss Jim Jefferies brought on Graeme Owens and Allan Russell for Invincibile and Hamill respectively and the home side went in search of an equaliser.
With eight minutes remaining Taouil had a decent effort from 30 yards which went wide and then stopper Frazer Wright flicked the ball over the bar following a Hay corner.
But the Rugby Park men did not really make Olejnik work too hard and now find themselves firmly in the relegation zone.