How does Henry James influence Flannery O'Connor?

I’m assuming you are referring to O’Connor’s essay “The Nature and Aim of Fiction,” in which she discusses the various goals and characteristics of writing.
O’Connor mentions James by name, relating a story she heard about James’s repeated comment on any story he didn’t like. O’Connor states: “he would return it [to its author] with the comment, ‘You have chosen a good subject and are treating it in a straightforward manner.’” O’Connor explains that James’s remark is the ultimate insult to a fiction writer, because a true artist should be able to take the same subject that has been written about ad nauseam and address it in a fresh way.
Based on O’Connor’s body of work, it becomes clear that she agreed with James’s ideas about storytelling. For instance, “A Good Man is Hard to Find,” one of her most anthologized stories, wrestles with themes of family, sin, and forgiveness (oft referred to as grace in O’Connor’s case). While these are common literary themes, the author weaves a tragic, haunting tale full of humor and wit that is unique to this story alone.
Overall, James’s opinion of what makes a story “good” is reflected in O’Connor’s writing.