Heat coconut oil in a heavy-bottomed skillet over medium-low heat until shimmering. Add chicken. Cook, tossing to avoid sticking and burning, until no longer pink in the center, about 7 minutes. Move chicken to a bowl.

Combine onions, red bell pepper, jalapeno pepper, garlic, and ginger in the skillet. 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 flavors meld, about 30 minutes. Add kale, curry powder, salt, black pepper, and cilantro. Cook until sweet potatoes and carrots are soft, about 30 minutes more.