Cook rice according to package instructions. Meanwhile, in a large bowl, stir together 1 tablespoon cornstarch and 1/2 cup cold water until smooth. Add snow peas, garlic, ginger, sugar, soy sauce, and red-pepper flakes; toss to combine, and set aside.
In another bowl, whisk together egg whites, remaining 3 tablespoons cornstarch, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Add chicken, and toss to coat.
In a large nonstick skillet, heat 1 tablespoon oil over medium-high. Lift half the chicken from egg-white mixture (shaking off excess), and add to skillet. Cook, turning occasionally, until golden, 6 to 8 minutes. Transfer to a plate; repeat with remaining oil and chicken, and set aside (reserve skillet).
Add snow-pea mixture to skillet. Cover; cook until snow peas are tender and sauce has thickened, 3 to 5 minutes. Return chicken to skillet (with any juices); toss to coat. Serve with rice.