For a gas grill, light the front burner to medium-high and the back burner(s) to medium. For a charcoal grill, light a medium-high fire (400°F) with two-thirds of the coals banked to one side. Clean and oil the grill grates.
In a small bowl, mix 1-1/2 tsp. salt and 1 tsp. pepper with the allspice, cinnamon, and chipotle powder. Sprinkle the chicken all over with the spice rub. Sprinkle the chiles and scallions with 1 Tbs. oil, 1/2 tsp. salt, and 1/2 tsp. pepper.
Set the chicken over the hot zone of the fire, and the chiles and scallions over the cooler zone. Grill until the chicken, peppers, and scallions have good grill marks, 3 to 4 minutes. Continue to grill the peppers and scallions until they brown and become just tender, about 3 minutes more. Grill the chicken, flipping as needed, until it is firm to the touch and cooked through (slice into a thicker piece of the chicken with a knife to check), 6 to 8 more minutes. Transfer the chicken and vegetables to a large cutting board to cool. Coarsely chop the chicken, peppers, and scallions.
In a large serving bowl, toss the mango with the chicken, peppers, and scallions. Add the lime juice and the remaining 2 Tbs. oil and toss well. Season with more lime juice, salt, and pepper if needed. Serve immediately.