In a large bowl combine chicken pieces and poultry seasoning; toss to coat. In a 4-quart Dutch oven heat oil over medium heat. Add chicken pieces; cook for 3 to 5 minutes or until chicken pieces are browned. Using a slotted spoon, transfer chicken to bowl and set aside.
In the same Dutch oven cook onion, celery, carrot, and garlic over medium heat about 5 minutes or just until tender, stirring occasionally. Add chicken broth; bring to boiling. Add chicken, noodles, and zucchini. Return to boiling; reduce heat. Simmer, covered, for 5 minutes.
In a medium bowl whisk together milk and flour until combined; stir into chicken mixture. Cook and stir until bubbly. Cook and stir for 1 minute more. Sprinkle with parsley just before serving.