MacKinnon, who has 28 points (nine goals, 19 assists) during his streak, also set a new single-season NHL career high with 113 points (41 goals, 72 assists).
Mikko Rantanen had two goals and two assists, and Valeri Nichushkin had a goal and two assists for the Avalanche (41-20-5), who have won four in a row and six of seven. Justus Annunen made 25 saves.
Daniil Miromanov and Walker Duehr scored for the Flames (31-29-5), who have lost three straight and four of five after a season-long five-game winning streak. Dan Vladar allowed six goals on 35 shots before he was replaced by Dustin Wolf at the start of the third, who saved all three shots he faced.
Colorado scored five unanswered goals in the second period to erase a 2-1 deficit.
Josh Manson tied it 2-2 at 4:52 with a slap shot from the right point.
MacKinnon put the Avalanche up 3-2 at 5:50 with a one-timer from the left face-off circle over Vladar's left shoulder.
Nichushkin extended it to 4-2 at 7:53, taking a cross-ice pass from Rantanen and scoring with a snap shot in the slot.
Casey Mittelstadt pushed it to 5-2 at 14:10. He shot past Vladar's blocker on a partial breakaway set up by Brandon Duhaime in the neutral zone for his first goal for Colorado since he was acquired in a trade with the Buffalo Sabres on March 7.
Rantanen made it 6-2 at 19:14 with a snap shot from a tight angle below the left circle after Cale Makar’s shot hit the post.
Rantanen gave Colorado a 1-0 lead at 2:05 on the power play, putting in a cross-crease pass from Nichushkin.
Miromanov tied it 1-1 at 3:24 when he beat Annunen with a slap shot from the point. The goal is Miromanov's first this season, and first with Calgary after he was acquired in a trade from the Vegas Golden Knights on March 6.
Duehr gave Calgary a 2-1 lead at 6:46, scoring his first goal in 31 games when he beat Annunen with a backhand in the slot off a 3-on-1 rush.
