In small bowl, whisk together coconut milk, peanut butter, vinegar, 1/2 teaspoon of the salt and the red-pepper flakes.
In large skillet, heat oil over medium-high heat. Season both sides of chicken breasts with remaining 3/4 teaspoon salt and the black pepper. Add chicken to skillet; cook 4 minutes. Flip chicken over; cook until internal temperature registers 170 degrees F on instant-read thermometer, 4 to 5 minutes. Transfer to plate; cover and keep warm.
Cook cappellini in large, deep pot of lightly salted boiling water until al dente, firm yet tender, following package directions. Drain.
Meanwhile, place skillet over medium heat. Add 1 bag of coleslaw mix, the scallions and 2 tablespoons water; cook, stirring frequently, 2 minutes. Add second bag of coleslaw mix; cook 2 minutes.
Slice chicken into thin strips. Stir half of the chicken strips and the coconut-peanut sauce into the vegetables in the skillet; cook until slightly wilted, 2 minutes. Transfer to large bowl.
Add cappellini to the chicken mixture; toss to mix well. Top with the remaining sliced chicken and chopped peanuts. Serve immediately. Makes 8 servings.