Cook ground chicken in a large skillet over medium heat, stirring constantly to break it into small crumbles, about 5 minutes. Stir in peanuts, red pepper flakes, ginger, and salt. Add lime juice and fish sauce. Cook, stirring occasionally, until liquid evaporates and chicken appears dry, about 10 minutes.
Transfer chicken mixture to a large bowl. Fold in mint, basil, and cilantro. Spoon mixture into individual butter lettuce leaves and top with cucumber.
