Flamini rejoined the Gunners from AC Milan over the summer having previously left in 2009.
Parlour has now credited the 29-year-old with adding a much-needed steeliness to the team.
"Flamini has been very important," he told the club's official website. "At times over the last few seasons when Arsenal have broke forward they look great but when they lose the ball they have been very open in midfield. Good teams will exploit that.
"He's always in those areas where the ball breaks loose and is always trying to win the ball back. He then moves it quickly to the likes of Jack Wilshere and Mesut Ozil who can really do something with the ball."
Arsenal return to Premier League action on Saturday when they entertain Norwich City at the Emirates Stadium.