Scott Arfield gave Falkirk the lead against the run of play in the first half but Mickael Antoine-Curier's seventh of the campaign for Accies and Simon Mensing's disputed penalty eight minutes later had the visitors staring at another costly defeat.
However, Flynn popped up only three minutes later to rifle in when Hamilton failed to clear Pedro Moutinho's free-kick.
And only a magnificent last-ditch tackle from Martin Canning prevented Moutinho from sealing a rare win for the SPL's basement side.
Flynn is now targeting another positive result when the Bairns travel to face St Johnstone on Tuesday bidding to close the three-point gap to second-bottom St Mirren.
The former Liverpool youngster said: "We needed the goal. We started the second half really poorly and conceded two soft goals.
"We just had to push on and luckily we got that goal straight away and bounced back.
"We took a point from the game but we're a bit disappointed we didn't take three points.
"We moved a point closer to St Mirren and we play on Tuesday night now so we've got a chance to get level with them then.
"There are nine games to go and so it's nine important games, games that are all winnable. We just have to keep pushing on.
"The most important game is always the next one and that's on Tuesday night now. We'll take the positives from Saturday's game and move on to Tuesday."
Flynn's sweet reverse pass set up Arfield for the opener after 25 minutes when the Scotland Under-21 midfielder beat goalkeeper Tomas Cerny at the second attempt.
Moutinho had the chance to add a second as the half drew to a close after Canning had left a clearance from Robert Olejnik but the Portuguese striker's lob drifted agonisingly wide.
It was a costly miss as Antoine-Curier headed in Flavio Paixao's corner four minutes after the break.
And the on-loan Dundee marksman was then controversially adjudged by referee Dougie McDonald to have been felled by Brian McLean - a decision which drew stinging criticism of officials from Pressley for the second week running - to allow Mensing to put Accies ahead from the spot.
Mensing revealed the Lanarkshire men's disappointment at not being able to hold on to their lead but insisted even victory would not have been enough to seal Hamilton's SPL status for another season.
Looking forward to Wednesday's clash with Kilmarnock as they bid to stretch a four-game unbeaten run, he said: "Was it a better point for us than Falkirk? Not being 2-1 up, no. I thought we were worthy of the three points, especially after going 1-0 down.
"That was frustrating because I thought we dominated the opening stages and their goal was against the run of play.
"But it's a positive that that's four games unbeaten now. There are more important games coming up. Your next game is always bigger.
"It's frustrating that we didn't get the three points but there are many more games left. Even if we had got the three points, it wouldn't have been a closed door.
"There's a long way to go yet and I'm just looking forward to the run- in."
Source: Team Talk