Combine flour and 1 teaspoon salt in a bowl. Dredge chicken pieces in the mixture.
Heat 1/4 cup olive oil in a large skillet with a lid over medium-high heat. Add chicken pieces; cook until browned on all sides, 6 to 8 minutes. Add tomatoes, artichoke heart liquid, green bell pepper, mushroom liquid, and garlic. Add remaining 2 tablespoons oil, vinegar, and bay leaf.
Reduce heat and simmer chicken until flavors start to blend, about 10 minutes. Add red wine, lemon juice, parsley, salt, and pepper. Cover and continue simmering until chicken is tender and no longer pink at the bone, about 30 minutes more. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C). Stir in artichokes and mushrooms; cook until heated through, about 5 minutes.