In a medium saucepan over medium-high heat, warm the oil until hot but not smoking. Add the scallions and cook, stirring, until they begin to brown, 2-3 minutes. Stir in the flour and cook, stirring, until the flour is no longer visible, about 30 seconds.
Add the chicken broth and rice, cover, and bring to a boil over high heat. Reduce the heat to medium-low and cook, partially covered, until the rice is tender, about 20 minutes.
Add the chicken, corn, dill, and pepper. Return the chowder to a boil, then reduce to a simmer and cook, stirring constantly, until the chicken is cooked through, about 5 minutes.
Stir in the beans and milk and cook until the beans are heated through, about 1 minute.