Add the oil to the saute pan over medium hight heat. Dredge the chicken in the flour, coating on all sides. Shake off the excess flour and put them into the pan, skin side down. Cook until brown, then turn the pieces over and brown the other side. Remove the chicken pieces and put them on a warm plate. Season with salt and pepper.
Turn the heat back up to medium high and add the sliced onion to the pan. Cook until the onion is deep golden. Add the wine and deglaze the pan for about 30 seconds, scraping the tasty brown bits (fond) up from the bottom of the pan.
Add chicken thighs and legs to the pot along with the red and yellow bell pepper, mushrooms, carrots, celery, garlic, and diced tomatoes. Cook at a slow simmer with the lid on for about 20 to 30 minutes. Add the chicken breasts and cook for another 10 minutes.
Remove the chicken and put on a serving platter. If the sauce is a bit watery, turn the heat up to high and cook uncovered until the sauce thickens a bit. Serve the sauce and chicken together.