Heat remaining 1 tablespoon oil in skillet over medium. Add carrots, celery, and onion; cook, stirring often, until vegetables are softened, about 8 minutes. Add 1/4 cup of the flour; cook, stirring constantly, until vegetables are fully coated, about 30 seconds. Add chicken broth, and bring to a boil over medium-high; cook, stirring often, until slightly reduced and thickened, about 10 minutes. Transfer mixture to slow cooker, and stir to combine with chicken.