Preheat the oven to 350 degrees F (175 degrees C). Season chicken with salt and pepper.

Heat oil in a large cast iron skillet over medium heat. Add garlic and red pepper flakes; cook and stir until garlic is soft and fragrant, 1 to 2 minutes. Add chicken and brown for about 3 minutes per side.

Transfer the skillet to the preheated oven and bake until chicken is no longer pink at the bone and the juices run clear, 7 to 10 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).

Bring apricot nectar to a boil in a large pot over medium-high heat, then reduce then heat to medium-low. Mix water and cornstarch together in a small bowl; stir into apricot nectar. Stir in curry powder, then apricots. Add baked chicken.

Place the cast iron skillet with chicken drippings over medium heat. Stir in carrots, onion, bell pepper, and chile pepper; cook and stir until onion is translucent, about 5 minutes. Pour chicken and apricot sauce into the skillet; cover and simmer until vegetables are tender, about 10 minutes. Season again with salt and pepper. Stir in water chestnuts just before serving.