In a large bowl, mix egg, garlic, chicken, panko, and 2 Tbsp. chives; season with salt and pepper. Roll into small balls (about the size of golf balls).
In a medium bowl, whisk hot sauce, brown sugar, vinegar, and red pepper flakes; season with salt.
In a large skillet over medium heat, heat oil. Arrange meatballs in a single layer and cook, turning occasionally, until seared all over, 3 to 4 minutes per side. Add sauce and bring to simmer. Cook, stirring occasionally, until sauce has slightly thickened and an instant-read thermometer inserted into meatballs registers 165°, about 10 minutes.
Transfer meatballs and sauce to a platter. Top with remaining 2 Tbsp. chives.