The flashbacks are the brother's memories that recur at specific points in his narration with the purpose of advancing the development of character and theme.
Interestingly, the author of "Sonny's Blues," James Baldwin, composed songs for Ray Charles and was a close friend of trumpeter Miles Davis. These facts explain the musicality of Baldwin's story, in which recurring motifs are employed along with the flashbacks. These flashbacks clarify at meaningful points in the narrative the brothers' relationship, Sonny's history, and the understanding that the narrator and his brother reach.
Perhaps one of the most significant flashbacks is the memory of the narrator's daughter Grace, whose death has brought the narrator to an understanding of his brother's pains—"My trouble made his real." Another significant memory is the narrator's recollection of his mother's plea that he look out for Sonny. His mother's tale about her husband's brother (the uncle) who was senselessly killed particularly moves the narrator because, like Sonny, the uncle was musical and had trouble "getting through this world."
Indeed, it is the flashbacks/memories that lead the brother to an understanding of Sonny and a willingness to accompany him to the nightclub, where he sits in the dark corner and listens to Sonny's music, the "personal, private, vanishing evocations." In this club, the brother experiences an emotional moment of understanding:
But the man who creates the music is hearing something else, is dealing with the roar rising from the void and imposing order on it as it hits the air. What is evoked in him, then, is of another order, more terrible because it has no words, and triumpant, too, for that same reason. And his triumph, when he triumphs, is ours.
Further, the brother/narrator describes the glass that the waitress puts on top of the piano for Sonny as glowing and shaking "above my brother's head like the very cup of trembling," a symbol of Sonny's trouble and suffering that rests above the music he plays beneath it. This music carries meaning to the brother, who understands its meaning. Sonny's "triumph" is both brothers' "triumph" as they rescue their relationship.