Preheat an oven to 180 degrees C. Season the chicken drumsticks with salt and pepper.
Heat olive oil in a large oven-safe frypan over medium heat. Stir in garlic and chilli flakes. Cook and stir until garlic is softened and is fragrant; 1 to 2 minutes.
Place the drumsticks in the frypan and brown the chicken on all sides; about 3 minutes on each side. Transfer the frypan to the oven.
Bake the chicken drumsticks in the preheated oven until no longer pink at the bone and the juices run clear; 7 to 10 minutes.
Bring the apricot nectar to a boil in a large saucepan over medium-high eat then reduce heat to medium-low.
Mix cornflour and water together in a small bowl then stir into the mixture along with the curry powder into the apricot nectar. Add dried apricots. Transfer the baked drumsticks into the apricot mixture.
Heat the frypan used to cook the chicken over medium heat. Stir in the onion, capsicum, carrots and chilli then cook and stir until the onion has softened.
Pour the drumsticks and apricot sauce into the frypan. Cover and simmer until the vegetables are tender; about 10 minutes.
Season with salt and pepper. Stir in water chestnuts just before serving.