Make marinade for chicken by combining, basil, mint, and cilantro in a food processor bowl. Add lime juice, ginger, garlic, soy, fish sauce oil, and honey. Process until smooth. Remove marinade from processor into ziplock bag and add red pepper flakes. Place chicken in bag, seal bag, and marinate for at least 2 hours or overnight.
In a bowl, combine all dressing ingredients. Reserve.
Place noodles in a large bowl, cover with boiling water. Let stand until softened, about 4 minutes. Drain and rinse under cold water. Drain again well. With a knife or scissors inserted into bowl, cut noodles several times.
Heat grill on medium high. Remove chicken from marinade and discard marinade. Place on heated grates and grill for about 5-6 minutes per side or until chicken registers 165 degrees F on an instant read thermometer. Remove chicken from grill.
Place noodles in bowl. Pour reserved dressing over noodles and toss. Add basil, mint, cilantro, snow peas, tomatoes, carrots, and scallions. Toss well until combined. Divide among four soup plates.
Slice each chicken breast crosswise into 1-inch strips. Place chicken slices on top of noodles in each bowl. Sprinkle with peanuts and garnish with lime wedges. Serve immediately.