Season the chicken with smoked paprika, oregano, ½ teaspoon salt, and black pepper.
Heat the olive oil in a large skillet over medium-high heat. Add the chicken in a single layer and cook for 4–5 minutes, turning occasionally, until browned on the outside. Transfer the chicken to a plate.
Reduce the heat to medium and add the onion. Cook for 2–3 minutes, then add the garlic and ginger and cook for another 30 seconds.
Stir in the tomato paste and turmeric and cook for 1 minute.
Pour in the chicken broth, scraping up any browned bits from the bottom of the skillet. Add the coconut milk, remaining salt, and red pepper flakes if using.
Bring the sauce to a gentle simmer and cook for 3–4 minutes, until slightly thickened.
Return the chicken and any accumulated juices to the skillet. Simmer for 4–5 minutes, stirring occasionally, until the chicken is cooked through and the sauce coats the pieces.
Divide the cooked rice between four bowls. Spoon the coconut chicken and sauce over the rice.
Top with cucumber, cilantro, green onions, and toasted coconut flakes if using. Serve with fresh lime wedges for squeezing over the bowls.