In a large skillet, melt 1/4 cup of the butter over medium heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for 6-7 minutes on each side, or until the chicken is golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining butter and olive oil. Sauté the minced garlic and red pepper flakes for about 1 minute, or until fragrant. Pour in the chicken broth and white wine, scraping up any browned bits from the bottom of the skillet. Bring the mixture to a simmer and let it cook for 5 minutes.
Stir in the lemon juice and chopped parsley, then return the chicken to the skillet. Let it simmer for an additional 5 minutes, allowing the flavors to meld.