Mix the flour, white pepper, oregano, and basil together on a plate.
Wash and dry the chicken breasts and coat each with the flour mixture. Reserve any leftover flour.
Heat the oil and butter in a frying pan. Add the chicken breasts and sauté gently until brown and tender on both sides, about 15 minutes. Remove the breasts to a dish.
Add the mushrooms and 1/4 cup of the wine; cook for about 5 minutes over low heat. Scrape the bottom of pan to loosen any flour. Stir in any reserved flour and the remaining wine.
Simmer until the mixture thickens, stirring constantly. Slip the cooked breasts into the sauce. Cook gently for about 5 minutes or more.
