Season the chicken pieces with salt and black pepper.
Place the flour in a shallow bowl. Press each chicken piece into the flour and tap off excess.
Heat the olive oil in a large Dutch oven over medium heat until almost smoking hot.
Pan-fry the chicken until golden brown on both sides, about 3 minutes per side. Work in batches so as to not overcrowd the pan. Set the browned chicken aside.
Stir the onion, green bell pepper, and garlic into the Dutch oven; cook, stirring occasionally, until tender, about 5 minutes.
Stir in the mushroom; cook until they release their juice, 5 to 8 more minutes.
Mix in oregano, tomatoes, tomato paste, white wine, and chicken stock; bring to a boil.
Return the chicken pieces to the sauce, cover the pan, reduce heat to medium-low, and simmer until the chicken is no longer pink inside and the juices run clear, 30 to 40 minutes.