The climax of the story is when Sarty tries to warn someone that his father is going to burn down the barn, but stops.
Climax is a story’s turning point. It is the point where the initial problem is no longer an issue, and another problem becomes important. The character has to make a choice, and deal with the consequences. Either way, nothing is the same after the climax.
Sarty's conflict comes from the contradiction between what he thinks of his father and who he realizes his father has become. All his life, he has loooked up to his father. However, when he finds out that his father really is an arsonist, Sarty has little respect for his father, Abner. His family gets run out of town because his father is a firebug who cannot control his emotions. He seems to start fires as revenge for perceived wrongs, putting his family at risk.
When the family moves to the home of Major de Spain, it is not long before an altercation develops. Abner won’t take his shoes off, so he soils an expensive rug. When they force him to clean it, it gets destroyed. Major de Spain then wants him to pay for it. Abner is annoyed, and decides to burn the barn.
Abner is aware that if Sarty gets loose he will give warning, so he tells his family to tie him up.
“… Take hold of him. I want to see you do it." His mother took him by the wrist. "You'll hold him better than that. If he gets loose don't you know what he is going to do? He will go up yonder."
Sarty does try to get free, and give warning. He does not care what it will do to his father. He is frustrated with his father and what he has done to the family. As he is running, he hears shots. He assumes his father has been shot. Despite his choice earlier, he feels bad.
The conflict here is both external and internal. Sarty never really gets to make his choice. It is taken from him. First his father stops him, and then he does not get there in time. Would he have told? Should he have taken a more direct route? Sarty will never know, and he has to live with that uncertainly. Since Sarty never got resolution, he never knows what he would have done.