Place the carrots, celery, onion, and olive oil in a 6-quart Dutch oven to the soup pot. Allow the carrots, celery, and onion simmer over medium heat for 10 minutes or until the onions are translucent.
Add the garlic cloves, chicken stock, water, and 1 cup of milk to the mixture and mix.
Add the pepper, dried oregano, bay leaf, and chicken. Mix until combined. Allow the soup to simmer over medium heat for 15 minutes.
Whisk together the other 1 cup of milk with the ½ cup flour until smooth. Place into the soup mixture and whisk until combined.
Place the long grain and wild rice and the seasoning packet into the soup and mix until combined. Allow the soup to simmer for 20 minutes or until the rice is tender. Add salt and pepper to taste.