Make the marinade: combine the oil, lime juice, garlic, honey, cumin, coriander, red pepper flakes, chopped cilantro, salt, and pepper, in a large bowl, until the honey dissolves. Place the chicken in the bowl, toss to coat, cover, and refrigerate for 30 minutes.
Make the salsa: place the mango, avocado, tomatoes, red onion, and cilantro in a bowl. Add lime juice, salt, and pepper. Toss to mix.
Heat a large skillet over medium-high heat and brown the chicken breasts for 2 minutes on each side. Pour in the marinade, lower the heat, and cook, covered, until fully cooked, about 3 minutes. Serve with a side of rice and with mango-avocado salsa on top.