Fill a large pot with lightly salted water and bring to a rolling boil; stir in vermicelli and return to a boil. Cook uncovered, stirring occasionally, until tender yet firm to the bite, 4 to 5 minutes. Drain.
Heat 2 tablespoons oil in skillet. Add coleslaw mix. Cook, stirring occasionally, until browned, 8 to 10 minutes. Add green bell pepper, peas, and green onions. Cook until softened, 4 to 5 minutes. Add 1 tablespoon ketchup and soy sauce; cook until warmed through, about 5 minutes. Remove from heat.
Heat remaining 3 tablespoons oil in a separate skillet. Add chicken, salt, and ginger-garlic paste. Cook, stirring frequently, until no longer pink in the center and the juices run clear, about 10 minutes. Stir in remaining 2 tablespoons ketchup, 1/2 the tomato sauce, 1 cup water, 1 teaspoon red pepper flakes, coriander, and cumin. Cook and stir until heated through, about 5 minutes.
Mix 2 1/2 tablespoons water and cornstarch together in a bowl. Add to the chicken mixture. Cook until thickened, 3 to 4 minutes. Combine chicken mixture and coleslaw mixture.
Layer cooked white rice in the bottom of a 9x13-inch baking pan. Cover rice with the chicken-coleslaw mixture. Top with the cooked vermicelli.
Mix mayonnaise, 1/2 cup ketchup, and remaining 1/2 teaspoon red pepper flakes. Spread sauce on top of vermicelli.