Heat coconut oil in a heavy-bottomed pan over medium-low heat until shimmering. Add chicken. Cook, tossing to avoid sticking and burning, until no longer pink in the centre, about 7 minutes. Transfer chicken to a bowl.
Combine onions, red pepper, jalapeno pepper, garlic and ginger in the pan. Cook and stir until vegetables are softened, about 7 minutes. Add sweet potato, plantain and carrots. Cook, stirring occasionally, until slightly tender, about 5 minutes.
Pour coconut milk, tomatoes and water into the vegetable mixture; stir to combine. Cook, covered, until flavours meld, about 30 minutes. Add kale, curry powder, salt, black pepper and coriander. Cook until sweet potatoes and carrots are soft, about 30 minutes more.