In a small bowl, combine the first 5 ingredients; set aside. Place flour in a shallow bowl. Add chicken, a few pieces at a time, and toss to coat; shake off excess. In a large skillet, heat 2 tablespoons oil over medium-high heat. Brown chicken on both sides. Remove from pan. Add mushrooms and onion to same pan; cook and stir until tender, 6-8 minutes., Add dressing mixture, stirring to loosen browned bits from pan. Return chicken to pan; bring to a boil. Reduce heat; simmer, uncovered, until a thermometer inserted in chicken reads 165°, 12-15 minutes longer.