Bayern also scored through an early own goal and through Leon Goretzka just before halftime to seal a meeting with reigning UEFA Champions League winners Paris Saint-Germain, who defeated Inter Miami 4-0 earlier Sunday.
Gerson and Jorginho scored for Flamengo, which became the second of four Brazilian teams eliminated after Botafogo lost in extra time to domestic rivals Palmeiras on Saturday.
After defeating Chelsea 3-1 in Group D play, the Rio de Janeiro side were resilient after going behind by two early.
But Kane’s second goal in the 73rd minute ultimately sealed Bayern’s passage and Flamengo’s first defeat in 11 matches across all competitions.
Joshua Kimmich fed Kane just above the penalty arc following a sloppy Flamengo giveaway. The Englishman turned slickly, then fired a low, right-footed effort into the bottom right corner for his 41st goal in all club competitions this season.
An early second-half penalty brought Flamengo back into the game.
Referee Michael Oliver pointed immediately to the spot after a Flamengo cross from the right struck Michael Olise’s outstretched arm.
Jorginho powered in a confident penalty to rouse the majority of the crowd supporting one of Brazil’s most decorated clubs.
Bayern started brightly and were quickly 2-0 in front.
In the sixth minute, Kimmich’s in-swinging corner from the right skimmed off the head of defender Erick Pulgar, who couldn’t get high enough in traffic to clear the ball and instead redirected accidentally inside the far post.
Three minutes later, Dayot Upamecano’s excellent challenge forced Giorgian de Arrascaeta into a turnover. Kane picked up the ball, drove briefly toward goal then unleashed a low shot from 22 yards that took a deflection on its way into the bottom left corner.
Flamengo responded in the 33rd minute, with Gerson reaching Luiz Araujo’s layoff and powering a first-time half volley past Manuel Neuer.
But Goretzka restored Bayern’s two-goal advantage eight minutes later when he guided his finish from beyond the box through traffic into the bottom left corner. (Reuters)