In "The Leap," what does the author’s use of flashback add to the story that a strict chronological telling would not accomplish?

The story is told by a narrator, not the principal character in the flashbacks.  The narrator, unlike Anna, the principal character, would not tell the story of her heroic, courageous actions as a mother the same way that a grateful daughter can and does.

She recalls her mother's life, as it relates to her, saying that her mother saved her three times, that is how the story is told through the unveiling of the three incidents.

The three flashbacks begin before the narrator was born, when Anna tried to protect her then unborn child, not the narrator, when lightening struck during her highwire act.  Anna chose to protect her unborn child, and not grab for her then husband's hand.

This led to the second flashback, when Anna went into the hospital before her baby was born, and met the narrator's father, a doctor.

The third flashback occurs when the narrator remembers her mother's courageous rescue of her from their burning house.  Anna never hesitated, even though the firemen believed that their was no rescue for the little girl in her upstairs bedroom. Anna uses her skills as a trapeze artist to swing onto the roof of the house, climb in the window and rescue her daughter.

Anna leaps out the window with her daughter held tightly against her body aiming for the fireman's net below.