Preheat oven to 375°F.
Season chicken breasts with 1 tsp of olive oil and 1 tsp of jerk seasoning each. Bake in oven for 20-25 minutes until cooked through. Allow to cool for 5 minutes, then dice and set aside.
While chicken is cooking, begin to assemble mango salsa. Toss together the diced mango, jalapeno, red onion, cilantro, lime juice, lemon juice and salt, stirring well. Set aside.
Heat a large pan to medium heat, and spray with cooking spray. Place one tortilla on the pan, and spread 1/6 of the shredded cheese, 1/6 of the diced chicken, and 1/6 of the mango salsa over half the tortilla. Fold the other half over and cook for 1-2 minutes, until the bottom is lightly browned. Gently flip, and cook the other side for another 1-2 minutes. Remove from pan.
Repeat with remaining tortillas until all are cooked.
Slice each quesadilla into 3 or 4 wedges, and serve!