Put rice into a medium bowl and pour in cold water to cover. Agitate rice with your hands until the water turns cloudy; drain and repeat this until water is almost clear, about 4 times. Add water until rice is covered by 2 inches and let soak for 30-45 minutes
While the rice is soaking, heat oil in a heavy pot (Dutch oven) over medium-high. Add shallot and cook until golden. Add garlic and cook until softened, about 1 minute
Add chicken, turmeric, cayenne, and 1.5 tsp salt. Cook, turning and moving chicken thighs as needed, until chicken begins to turn opaque, about 2 minutes. Pour in 3/4 cup water and bring to a simmer. Reduce heat to low, cover, and simmer for about 20 minutes, turning chicken once. Chicken should be cooked through and very tender after this stage
Drain rice and add to pot with chicken, then add coconut milk and remaining 1 tsp salt. Stir to incorporate and bring to a boil. Cover, reduce heat to lowest setting, and cook undisturbed for about 15 minutes, until rice is cooked well
Remove from heat and stir in kale. Re-cover and let sit until wilted, about 10 minutes
Divide chicken and rice among bowls and top with chilies