In a large bowl, whisk together the coconut milk, soy sauce, brown sugar, fish sauce, garlic, ginger, red pepper flakes, and lime juice until well combined.
Add the chicken pieces to the marinade, ensuring they are fully coated. Cover and refrigerate for at least 1 hour, or up to 4 hours for more flavor.
Preheat your grill to medium-high heat. If using wooden skewers, thread the marinated chicken onto the skewers.
Place the skewers on the grill and cook for 10-12 minutes, turning occasionally, until the chicken is cooked through and has nice grill marks. The internal temperature should reach 165°F.
Remove the skewers from the grill and let them rest for a few minutes before serving.