HEAT 2 tablespoons oil in large, nonstick saucepan over medium heat. Add onion and chile pepper; cook, stirring frequently, for 2 minutes. Add chicken, black pepper and red pepper flakes; cook, stirring frequently, until chicken is lightly browned and no longer pink. Remove chicken mixture to bowl; set aside.
HEAT remaining oil in same saucepan over medium heat. Add rice; stir to coat well. Microwave broth in 1-quart microwave-safe measuring cup on HIGH (100%) power for 3 1/2 to 4 minutes or until very hot.
ADD hot broth to rice small amounts at a time, stirring constantly. Allow each addition of broth to be absorbed before adding more. Once broth is gone, add evaporated milk in the same manner, stirring until absorbed. The process will take between 25 to 35 minutes. When the rice soft, stir in reserved chicken mixture and mushrooms. Rice should be creamy, not soupy.