Place chicken between two sheets of wax paper and pound to approximately 1/4-inch thick. In a large bowl or plastic bag, combine flour with next 3 ingredients. Add chicken to flour mixture, toss to coat.
Heat 2 tablespoons oil in a large skillet over medium-high heat. Sauté chicken 3-5 minutes per side or until done. Remove from skillet.
Add mushrooms and remaining oil, if needed. Sauté 2-3 minutes. Stir in wine and remaining 3 ingredients. Stir to loosen any browned particles; bring to a boil. Return chicken to skillet. Simmer, uncovered, 2 minutes.