Toss cubed chicken breast with flour until evenly coated.
Heat a skillet on medium-high heat, add 1 tablespoon of oil. Brown the chicken for about 8-10 minutes, then remove and set aside.
In a small bowl with remaining flour, mix chicken broth and soy sauce well, set aside.
In the same skillet, add rest of the oil, broccoli, onion, red pepper and mushrooms. Stir until softened, about 10 minutes.
Pour soy sauce mixture on vegetables and bring to a boil, stirring constantly. Toss in chicken, mix well and cook until sauce begins to thicken, about 10 minutes. Serve over rice.