Sprinkle cornstarch, salt, and pepper over flank steak. Refrigerate for 10 minutes.
Heat oil in a skillet over medium-high heat. Cook steak in the hot oil until lightly browned, 3 to 5 minutes per side. Remove steak from skillet using a slotted spoon.
Add onion and garlic to the same skillet. Cook until onion starts to soften, about 2 minutes. Add ginger; cook until lightly browned, about 1 minute. Add soy sauce, brown sugar, and hoisin sauce. Cook until sauce has thickened, 5 to 7 minutes more. Reduce heat; add green beans and bell pepper.
Add steak back to the skillet; toss in the sauce until well coated. Add red pepper flakes. Reduce heat to medium-low and cook and stir until stir-fry is heated through, about 5 minutes more.