Season chicken with salt and pepper. Heat oil in a Dutch oven or 12-inch skillet over medium-high heat until lightly smoking. Add chicken and cook until browned on both sides, about 6 minutes total. Transfer chicken to a plate.
In the same pot over medium heat, add shallot and cook, stirring frequently, until softened, about 2 minutes. Stir in red pepper flakes, cumin, and curry powder and cook until fragrant, about 30 seconds. Add broth and nestle chicken back into the pot. Adjust heat to maintain a gentle simmer and cook until the chicken is cooked through, about 5 minutes; season with salt and pepper. Using a slotted spoon, transfer chicken to a clean plate. Allow cooking liquid to reduce slightly, about 5 minutes.
Meanwhile, using two forks, shred chicken. Return chicken to pot and stir to combine with cooking liquid. Cook until chicken is warmed through, then remove from the heat.
Place kale in a heatproof serving bowl and pour chicken and its cooking liquid on top, tossing to combine. Stir in coconut, cherries, and lime juice, season with salt and pepper, and serve.
Credit Recipe and photo: Serious Eats