Dynamic characters are characters who change during the story; characters who don't change are static. Flat characters are characters that are one-dimensional; that is, they aren't fully developed. Characters who are developed fully so the reader sees their good points, their bad points, and their motivations are called round characters.
In "Barn Burning," the dynamic character is Sarty. At the beginning of the story, Sarty is fiercely loyal to his father. When his father strikes him, even though he didn't tell the men at the hearing that his father set the fire, Sarty doesn't talk back. As the story progresses, Sarty begins to see his father for what he is, and he cannot support him any longer. At the end of the story, he warns Mr. de Spain about the fire in defiance of his father and then runs away.
Abner Snopes, however, is a static character. He burns barns at the beginning of the story, and he burns them at the end.
The women in the story are particularly flat characters. The sisters are described as "big, bovine" and "hulking." Their size and appearance is given more attention than their thoughts or words, and they seem indistinguishable from each other. Indeed, Faulkner writes, "his father began to shout one of the sisters' names," without saying the name and without making a difference between the two girls. The mother, although she puts up a futile fight when Snopes goes out to burn de Spain's barn, is shown as a powerless female. Even Mrs. de Spain is a flat character. She is described as "a lady," and she acts like one, retaining her manners when treated with vile disrespect by Snopes, but as they leave, she emits "the hysteric and indistinguishable woman-wail." She is the flat stereotype of a lady.
Abner Snopes is round rather than flat; we get a picture of what motivates him and makes him tick. And Sarty is a round character.
Many of Faulkner's characters in the story are flat, especially the women, allowing the round and dynamic characters of Abner Snopes and Sarty to receive the reader's attention.