Whisk cornstarch and water together in a small bowl until dissolved. Combine soy sauce, sugar, mirin, ginger, garlic, and red pepper flakes together in a saucepan over medium heat until the mixture starts to simmer. Slowly whisk in cornstarch mixture. Bring to a boil; reduce heat to medium-low, and simmer until thickened, stirring often, about 10 minutes.
Pat chicken dry with paper towels; arrange in a baking dish. Pour sauce over chicken breasts, coating all sides.
Bake chicken breasts in the preheated oven until no longer pink in the center and the juices run clear, 25 to 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (75 degrees C).