When we think of plot diagrams and charting the plot of stories, the rising action are events that heighten the tension and exacerbate the central conflict of the text and lead to the climax, which is the moment of greatest emotional intensity in the story. If we take the climax of this excellent story to be when Doodle and his brother, in the storm, have to admit their failure to "train" Doodle and the brother abandons Doodle to his death, then the three points of rising action leading to this would be the following.
Firstly, I would argue the point when the narrator shows Doodle his coffin demonstrates the "knot of cruelty borne by the stream of love" that is present in their relationship, and also foreshadows the narrator's abandonment of Doodle at the end.
Secondly, when the narrator teaches his brother to walk and Doodle is able to give a demonstration of this to their parents, the narrator makes a very interesting and revealing confession when he admits that he taught Doodle to walk only because he was "ashamed" of having a crippled brother and that he was a slave of pride.
Lastly, and perhaps most importantly, the third incident of rising action occurs when the scarlet ibis descends on their tree and dies. The condition of the scarlet ibis, and how it dies, is explicitly linked to Doodle's death in the narrator's mind, as he recognises how Doodle, like the scarlet ibis, was a precious creature that needed protection and was not made for this planet.