The Spain international made the move to Camp Nou in 2011, but initially struggled to assert himself in the Blaugrana starting XI amid problems with fitness and form.
However, as he prepares to meet Fabregas in the last 16 of the Champions League on Wednesday, Flamini has claimed that the 25-year-old is being used well.
"He was always playing forward at Arsenal," he told the Catalans' official website. "I think his position at Barca allows him to express himself better and be more free.
"Fabregas remembers playing alongside Flamini fondly, ranking the Frenchman among his all-time favourite team-mates.
"I think the best things about Mathieu on the pitch are obviously the way he covers the ground, technically he’s really good, he doesn't lose the ball [and] he plays it simple," he added.
"I remember when we were playing together in 2007 and 2008, and for me it was amazing as he was running so much and covering a lot of ground for me to be more free and go forward, and play more combination passes for the team.
"He’s one of the best partners I made in football in my career. We played very well and we combined very well."
Flamini also warned his Rossoneri team-mates of the threat posed by Lionel Messi, who he believes to be the finest footballer on the planet.
"Barcelona are one of the better teams in Europe, with a great way of playing," he continued. "They are a great team with many talented players. "I agree, [Messi] is the best, he deserves all of his Ballon d’Or awards. He’s the best player in the game right now."