In a medium bowl, whisk together peanut butter, coconut milk, lime juice, soy sauce, brown sugar, ginger, garlic, and red pepper flakes until well combined.
Transfer 1 cup of the sauce to a small bowl, cover, and refrigerate until ready to serve. Set the remaining sauce aside.
Place chicken chunks in a large baking dish and cover with the remaining peanut sauce. Toss to coat well, cover with plastic wrap, and refrigerate for 1 to 8 hours, stirring once during marination.
Remove chicken from the fridge and thread onto skewers if using. Place skewers on a lightly greased baking sheet or place chicken on a wire rack set over a baking sheet.
To broil: Preheat broiler to high. Broil chicken for 6 minutes or until internal temperature reaches 160°F.
To grill: Preheat grill to medium-high (375° to 450°F). Grill chicken over indirect heat for 6 to 10 minutes per side until it reaches 160°F internally.
Serve the chicken with optional sides and room temperature reserved peanut sauce.