Father Flynn is the Catholic priest who arranges for the Guizacs to work on Mrs. McIntyre's farm. For most of the story we get the idea that Father Flynn approached Mrs. McIntyre with the idea. When she wants to fire Mr. Guizac she acts like hiring him was somebody else's idea. But she we learn that "She had never known a priest until she had gone to see this one on the business of getting her the Displaced Person" (3.5). This makes Mrs. McIntyre sound predatory, but also suggests that Father Flynn is active in helping refugees.
Father Flynn's accent suggests that he is also an immigrant, though we never learn his country of origin. His name suggests Ireland, but he could be from anywhere. We know for sure that O'Connor intends him as a "good guy" because of his intense admiration for the peacock. As you are probably aware by now, appreciating a peacock is definite sign of inner goodness in this story. (For more on the importance of peacocks to this story, check out "Symbolism, Imagery, Allegory.")
As we discuss in "Genre," O'Connor is also reacting against a tradition in Gothic literature to demonize Catholic priests and nuns. She doesn't think the Catholic church is perfect, and she doesn't ignore its problems. But she is expert at creating positive and interesting portrayals of Catholics, faults and all. While you might not agree with Father Flynn's attempts to convert Mrs. McIntyre to Catholicism, it's hard not to admire his dedication to helping refugees and immigrants.