Pound pork chops to 1/4-inch thickness. Season with salt and pepper, then lightly coat in flour.
Heat 2 tablespoons of the oil in a large skillet over medium-high. Saute chops until nicely browned on each side; set aside.
Add the remaining tablespoon of oil to the skillet. Cook mushrooms and onion, stirring occasionally, in the oil for about 5 minutes or until softened. Stir in 3 tablespoons of the flour.
Lower heat to medium; add soy sauce and vinegar. Cook about 1 minute, then add 1/2 cup water. Stir and cook about 2 minutes until the sauce is thickened. Add pork chops back to skillet, cover and cook 3-5 minutes longer. Garnish with cilantro if desired.