The veteran pair provide the Gunners with the foundation to be more efficient on the counter-attack, as well as affording advanced playmakers greater freedom to express themselves.
The partnership has inspired Arsenal to victories in the last two rounds of the FA Cup. The Arteta-Flamini axis was vital in overcoming both Liverpool and Everton and booking a place in the semi-final.
It has given manager Arsene Wenger's free-flowing team a necessary layer of structure in the middle. That power at the heart of midfield is something all of Wenger's trophy-winning teams had, but his recent squads have lacked.
When Wenger was sweeping all before him domestically, solid and complementary midfield duos were the platform for success. Emmanuel Petit and Patrick Vieira were the bedrock of the double winners in 1997/98.
Later it was Vieira and Gilberto Silva who helped the "Invincibles" win the English Premier League without defeat in 2003/04.
But since the departure of Vieira in the summer of 2005, Wenger has never got the power balance right in midfield. Flamini and Arteta, while not the most physically imposing pair, are tipping the scales in Arsenal's favor once again.
They give the Gunners two natural protectors for the defence. No other midfielders in the squad have their patience, authority and willingness to do the janitorial work the rest of this Arsenal team needs.
With an extra layer of protection behind the forward line and in front of the back four, attack-minded schemers have greater license to roam.
This was obvious and deadly in the 4-1 FA Cup quarter-final win over Everton. With Arteta and Flamini steadfastly guarding the middle, Santi Cazorla, Mesut Ozil and Alex Oxlade-Chamberlain could be more fluid.
The trio rotated positions at will. Ozil, ostensibly the No. 10 in the initial line-up, spent most of his time out wide, particularly on the left.
That let Cazorla drift more often into the middle, where he has performed best since signing at Arsenal in 2012. It also gave Oxlade-Chamberlain a roaming role Everton struggled to cover all game.
The freedom of movement enjoyed by Arsenal's three creative aces was made possible by the two-man defensive pivot behind them. Extra cover meant it wasn't always essential for the forward midfielders to hold positions to protect the structural integrity of the team.
Of course, Cazorla and Ozil still needed to track wide runners and support Arsenal's full-backs. This is something Ozil actually did with rare gusto.
But more freedom of movement behind the striker made Arsenal a more potent and inventive attacking force.
Usually, Arsenal rely on two of their central three, the most advanced midfielder, as well as a deeper player required to link defence and attack, to push forward.
Without Aaron Ramsey, who has been injured since Boxing Day, the Gunners have been missing a true link player. Jack Wilshere has pushed forward too often and without the precision timing Ramsey uses to outnumber defences on the break.
Wilshere has also neglected the need to drop in and cover space once Arsenal lose the ball.
Putting Arteta and Flamini together has given Wenger's team a true brain trust in the centre. Neither vacates his position for too long and never without the security of cover by the other.
As two natural organizers, Flamini and Arteta now give this team greater balance. That wasn't the case when the two were paired together earlier this season.
But now the right balance has been set, and it is one that promotes more ruthless counter-attacking. Arsenal's unforgiving streak on the break was evidenced by the way they savaged Everton, with three of their four goals coming on the counter.
Having one less midfield player roaming forward means Arsenal can cede more possession. But with an extra player at the base of midfield, the Gunners are better able to invite and absorb extra pressure.
Inviting it naturally promotes opportunities for quick counters. This is is where having one less man breaking forward is actually a case of "less is more" for Arsenal.
Without another player vying for the areas Ozil and Cazorla most often inhabit, the team's two best playmakers have more space to be creative.
Three midfield players supporting a lone centre-forward demands more efficiency in possession. Arsenal may see a little less of the ball when they play two deep midfielders, but they are doing more with it.
The perfect illustration of that was shown by the superb fourth goal against The Toffees. Cazorla won the ball and broke from deep, before spraying a pass out wide to meet Tomas Rosicky's supporting run.
His first-time ball connected with Ozil's gallop though the middle. The mercurial schemer then reversed a one-touch pass into the path of Giroud, who promptly tapped the ball into the net.
Three passes, a calm finish and a goal. That is what Arsene Wenger's teams looked like when they were great.
Breaks of that quality are only possible with true strength and stability in the middle. That barrier is what forces teams into the mistakes players like Cazorla can transition into counter-attacks.
The imminent return of Aaron Ramsey doesn't need to change this dynamic. Simply play Ramsey, who does his very best work in advanced areas anyway, ahead of Flamini and Arteta.
That leaves Oxlade-Chamberlain as excellent cover for both wide berths, occupied by Ozil and Cazorla, as well as the most advanced central position.
The Arteta-Flamini partnership gives Arsenal a level of solidity that can take them anywhere. It was originally thought to be an option reserved only for tough away fixtures.
While there are certainly enough of those left this season, Wenger should make the Arteta-Flamini partnership a permanent fixture.