In a large soup pot or Dutch oven, warm olive oil and butter at medium-high heat until melted together. Add veggies and cook to soften, at least 5 minutes. Sprinkle with flour and cook an additional minute, stirring constantly.
In a bowl, mix broth, cream, and milk together. Slowly add to veggie mixture. Add red pepper flakes, salt, and pepper. Combine with a whisk. Add chicken. Stir, turning the heat down to medium until everything is hot, about 10-15 minutes.
The longer it cooks, the better it tastes. Makes excellent leftovers.
Serve with biscuits and a salad.