In a shallow bowl, combine the flour, 1 teaspoon of the salt, and 1/2 teaspoon of the pepper. Rinse the chicken and pat it dry with paper towels. Working in batches, lightly coat the chicken with the flour mixture, shaking off any excess.
Heat the oil in a Dutch oven or large saucepan over medium heat. Add some of the chicken to the pan and cook until browned, 4 to 5 minutes per side. Transfer to a plate; set aside. Repeat with the remaining chicken.
Add the onion to the pan and cook for 2 minutes. Add the carrot, celery, garlic, thyme, and bay leaf. Cook, stirring occasionally, for 10 minutes.
Crush the tomatoes in the can with a large spoon and stir them into the vegetables along with the wine and the remaining salt and pepper. Bring to a simmer. Add the chicken, reduce heat, and cover. Simmer for 45 minutes, turning the pieces occasionally. Remove and discard the bay leaf. Stir in the parsley.