The midfielder collected the ball from Lucas Podolski and hooked in Arsenal's equaliser from the centre of the penalty box after 53 minutes.
City had taken the lead after 18 minutes when Edin Dzeko's close-range shot from a David Silva cross hit the post and the Spaniard tapped home the rebound for his seventh goal of the season. Flamini said: "We wanted to win. It was important for us and for the fans especially after the 6-0 defeat to Chelsea and the draw with Swansea on Tuesday.
"But unfortunately we came away with another draw. In the first half we saw there was the opportunity to create some goals so we came out for the second half and tried our best. We scored one goal and we tried to get another for the victory, but we missed the opportunity."
Liverpool host Tottenham today and now have their championship destiny in their own hands, with key clashes against City and Chelsea at Anfield still to come. City started brightly and Jesus Navas curled a 20-yard effort just wide. Tomas Rosicky went down inside the City box under a Pablo Zabaleta challenge after 12 minutes but while there looked to be some contact referee Mike Dean pointed for a goal-kick.
Arsenal started to ask more questions of the City defence, but the visitors were lightning quick on the break and swept into the lead.
When Lukas Podolski lost the ball in midfield Silva carried it forward to the edge of the Arsenal area before feeding Dzeko on the left. His shot cannoned back off the near post and landed at the feet of Silva, who sent it into far corner.
Arsenal were still very much in the match as the interval approached but City almost doubled their lead at the start of the second half when Wojciech Szczesny spilled Navas' low cross. The ball deflected off Arsenal defender Per Mertesacker but just the wrong side of the post.
Santi Cazorla's drive stung Joe Hart's hands before Arsenal levelled on 53 minutes. The ball was worked out to the left for Podolski, and his low cross was swept into the far corner by Flamini from 12 yards out.
Arsenal suddenly found another gear and a Bacary Sagna cross flew through the six-yard box before Hart somehow deflected a fierce angled drive from Podolski behind.
Arsenal continued to push on but City, always dangerous on the counter, were not about to throw away what could turn out to be a crucial point in their title quest.