Heat sun-dried tomato oil in a large pot over medium heat. Add onion and carrots; cook, stirring, until softened, about 4 minutes. Add garlic and Italian seasoning; cook, stirring for 1 minute. Add flour; cook, stirring, for 1 minute more. Add milk, broth, salt and pepper; increase heat to medium-high and bring to a simmer. Add zucchini and sun-dried tomatoes; cook, stirring occasionally and reducing the heat to maintain a simmer, until the zucchini is tender, about 8 minutes. Add spinach and chicken; cook, stirring, until the spinach is wilted and the soup is hot, about 2 minutes more. Remove from heat and stir in vinegar.