In 12-inch skillet, heat oil over medium heat. Cook onion, carrot and garlic in oil 5 to 7 minutes, stirring occasionally, until slightly tender.
Cook rice in water as directed on package; cover to keep warm.
Into mixture in skillet, stir mushrooms, frozen vegetables in sauce, stir-fry sauce and pepper flakes; cook 5 to 7 minutes, stirring occasionally, until vegetables are tender. Serve over rice.