Prepare the Alabama white sauce and chill it for at least 1 hour or up to 3 days before serving.
Trim excess fat if desired and cut each skin-on chicken thigh into strips, keeping pieces roughly equal so they cook evenly.
Thread the chicken strips onto 5 skewers, leaving a little space between pieces for even heat circulation.
Brush the skewered chicken with 1 tablespoon olive oil and season evenly with Kosher salt and black pepper.
Preheat your grill to medium-high heat.
Place the skewers over direct heat and grill, turning occasionally, until the skin is crisp and the chicken is cooked through, about 12–15 minutes.
Brush some Alabama white sauce over the chicken and grill 1 minute, flip the skewers, brush more sauce, and grill another minute; then remove from the grill.
Garnish with snipped chives and a sprinkle of red pepper flakes if desired, and serve immediately with remaining white sauce on the side.