Bring chicken broth to a boil in a medium saucepan over medium-high heat. Add the soy sauce, mirin, and sugars. Stir until sugars are dissolved. In a small bowl, combine cornstarch and water. Add to soy sauce mixture and continue to boil until sauce begins to thicken, about 5 minutes. Remove from heat.
Drain and discard chicken marinade. Add flour to chicken pieces and stir to coat.
Heat oil in a large skillet over medium-high heat. Working in batches, spread chicken pieces in a single layer in the pan. Cook until chicken begins to brown, about 3-5 minutes. Using a spatula, flip chicken pieces over to brown the other side.
Add ¼ cup of the teriyaki sauce to the pan. Cook for an additional 3-5 minutes, stirring often, until the sauce reduces and darkens in color and begins to coat the chicken. Remove chicken from the skillet and set aside.
Repeat with remaining chicken. Afterwards, return all the chicken to the skillet. Add another ¼ cup teriyaki sauce. Cook until chicken is heated through and coated with the sauce.
Serve chicken over hot white rice. Sprinkle with sliced green onions if desired.