Sprinkle the chicken pieces with 1 teaspoons of each salt and pepper. Dredge the chicken pieces in the flour to coat lightly.
In a large, heavy saucepan, heat the oil over a medium-high flame. Add the chicken pieces to the pan and sauté just until brown, about 5 minutes. If all the chicken does not fit in the pan, sauté it in 2 batches. Transfer the chicken to a plate and set aside. Add the bell pepper, onion, and garlic to the same pan and sauté over medium heat until the onion is tender, about 5 minutes.
Season with salt and pepper. Add the wine and simmer until reduced by half, about 3 minutes. Add the tomatoes with their juice, broth, capers, and oregano. Return the chicken pieces to the pan and turn them to coat in the sauce. Bring the sauce to a simmer. Continue simmering over medium-low heat until the chicken is just cooked through, about 30 minute for the breast pieces, and 20 minutes for the thighs.
Using tongs, transfer the chicken to a platter. If necessary, boil the sauce until it thickens slightly, about 3 minutes Spoon off any excess fat from atop the sauce. Spoon the sauce over the chicken, then sprinkle with the basil and serve.