To make the chicken, buzz the onion, garlic, ginger, coconut milk, lemon juice, salt, black pepper, and red pepper flakes in a food processor until smooth. Drop the chicken pieces into a ziploc bag and pour in the marinade. Place the bag in a shallow dish and marinate in the fridge for at least 4 hours, but overnight is better, turning several times.
To make the sauce, heat the oil in a large skillet over medium heat. Add the onion and cook, stirring often, until golden brown, about 7 minutes. Reduce the heat to low, add the lemon zest, ginger, red pepper flakes, and tomato paste, and cook, stirring often, until the colors deepen and the mixture is very fragrant, 8 to 10 minutes. Toss in garlic and cook for 1 minute more.
Pour in the coconut milk and cream and bring to a boil, e turn heat to low and simmer, uncovered, until the liquid has reduced by one quarter, about 10 minutes. Season to taste with salt and pepper. Cover and keep warm.
Meanwhile heat a grill to high. Remove the chicken from the fridge and let sit out for 30 minutes.
Lower the heat of the grill to medium and brush the grate with oil. Remove chicken from marinade and grill until well marked and cooked through, about 5 to six minutes per side.
To serve, slice each chicken breast into 3 pieces on the bias. Place cooked rice onto plates, top with chicken slices, and spoon sauce over top.