Heat 1 tbsp. oil over medium heat in a large, wide dutch oven or pot. Add onion, peppers, and oregano. Cook, stirring occasionally, until vegetables are softened and just beginning to brown, about 12 minutes. Reduce heat if vegetables begin to scorch.
Meanwhile, season chicken all over with salt and pepper and dust with the flour. In a large frying pan, heat remaining 1 tbsp. oil over medium-high heat. Add chicken skin side down and cook without moving until lightly browned, 5 minutes. Turn chicken over and cook until second side is lightly browned, 5 minutes more.
Transfer chicken to pepper mixture, arranging pieces on top. Drain fat from frying pan, add wine, and return to heat. Scrape up any browned bits, then pour wine into pot of chicken and peppers.
Adjust heat to maintain a simmer, cover, and cook until chicken is no longer pink at the bone, 12 to 14 minutes. Sprinkle with parsley.