What happens in the jazz club in "Sonny's Blues" regarding the brothers and Sonny's suffering?
The brothers in "Sonny's Blues" go to the jazz club after having a revelatory conversation in which the older brother listens to Sonny's point of view for the first time. He learns that Sonny believes that good can come from suffering, lessons can be learned, but only if the individual has a way to control the suffering. Sonny's playing at the jazz club illustrates this.
The other musicians give Sonny room to take the lead with the music in the first set they play, but Sonny lets it go by. Then in the next set, when he plays "Am I Blue," Sonny takes control of the music and thereby takes control of his suffering so that he can learn from it (one hopes he learns to rise above his circumstances and stay away from heroin and find a more beneficial course to take with his blues music), and in so doing rejoins the "family." His brother realizes that the blues has helped Sonny to protect himself from the drowning flood of suffering that came in torrents beginning in childhood.
The 1950s were a time when segregationist practices and racial prejudice all over America insured that African-Americans were outcasts with limited and restricted roads to success and happiness, even for those who followed a course like Sonny's brother chose. Racism then as now strangles children and youths so that the stifling choking erupts in violent anger then often erodes to despair and destructive escapism as it did for Sonny.