One must understand that not all short stories follow a typical plot line: introduction, rising action, climax, falling action, and conclusion. Sometimes, the climax, the falling action, and the conclusion all get wrapped into one.
In James Hurst's short story, "The Scarlet Ibis," the climax begins when Doodle is yelling to his brother not to leave him when the rain begins to fall. It is at this point in the story where the conflict between the brothers reach the highest point. Doodle's brother, trying to beat an oncoming storm, races in front of Doodle. Doodle, not being able to keep up, is left behind. Readers know that something misfortunate is about to happen. After returning to Doodle, the brother finds that Doodle has died.
Therefore, the climax comes when the story has reached its highest dramatic point. This is cued by the eminent storm and the threatening lightening. Doodle's brother begins to run and readers know that Doodle will not be able to keep up. The falling action and conclusion are intertwined at the close of the climax when Doodle's brother finds him dead. In reality, not much happens after the realization that Doodle has died. The story comes to an abrupt end, just as Doodle's life has come to an abrupt end.