The main conflict in “Barn Burning” is the character vs. character conflict between father and son.
A conflict is a struggle between opposing forces. They can be external or internal. An external conflict is a conflict between a character and an outside force. In a character vs. character conflict, two characters have a problem.
Sarty really admires and appreciates his father at the beginning of the story. He assumes that his father is being wronged. Unfortunately, Sarty has to learn that his father is not innocent. He really has been starting fires.
He could not see the table where the Justice sat and before which his father and his father's enemy (our enemy he thought in that despair; ourn! mine and hisn both! He's my father!) stood, but he could hear them, the two of them that is…
When they move yet again, and his father gets into a conflict again, Sarty realizes that his father is a barn burner. He decides to tell on him, to prevent him from burning another barn. Unfortunately, his father finds out and ties him up, and by the time he gets out it is too late.
The conflict between Sarty and his father is a character vs. character conflict because Sarty realizes his father is not someone to be admired, and because Sarty tries to prevent his father from burning another barn.
It is arguable that the main conflict is between Sarty and his father, Abner, if you read "Barn Burning" as a coming-of-age story. Sarty has to decide whether to be loyal to his father or follow his own moral compass.
However, another way to interpret the main conflict of "Barn Burning" is to consider Abner Snopes as a man in conflict with society.
As the story opens, Abner stands before the justice of the peace, accused of burning Harris's barn. Though the judge can't rule against him, he banishes Abner, who is only too glad to leave town and says something insulting about the town before leaving. Abner walks with a limp as a result of being shot as a horse thief in the Civil War by his "own people," the Confederates. These are two early indications that Abner has no use for society—and vice-versa.
Abner's pariah status is further explored as the story progresses. Initially, Sarty recognizes this in Abner, but he thinks of his father as having "wolf-like independence" rather than being an outcast.
Abner's deeply felt rage against Southern society stems from his social position. He is a white man in the South relegated to tenant farming. He resents how others prosper and feels increasingly disenfranchised; this leads to his offensive behavior against Major de Spain.