Preheat oven to 350°. Spread coconut on a rimmed baking sheet; toast, tossing occasionally, until golden brown, 8 to 10 minutes; cool.
In a medium bowl, whisk yogurt, cilantro, lime juice, chutney, mustard, turmeric, and cayenne; season with salt and pepper. Add chicken and mango, toss. Serve on spinach, sprinkled with coconut.