Whisk together olive oil, lime juice, minced garlic, honey, smoked paprika, cumin, salt, and pepper in a large bowl. Add chicken pieces, toss to coat thoroughly, cover, and refrigerate for at least 2 hours or overnight.
In a blender, combine mango chunks, brown sugar, apple cider vinegar, soy sauce, garlic, ginger, lime juice, and sriracha. Blend until smooth.
Transfer mango mixture to a small saucepan, bring to a simmer over medium heat, and cook for 8-10 minutes until slightly thickened. Remove from heat and stir in olive oil.
Preheat your grill to medium-high heat (approximately 375-400°F). For charcoal grills, arrange coals for indirect heat cooking.
Remove chicken from marinade and pat slightly dry with paper towels. Thread chicken, bell peppers, and red onion chunks onto skewers, alternating pieces and leaving small spaces between them.
Place skewers on the preheated grill. Cook for 4-5 minutes per side, rotating regularly until chicken reaches an internal temperature of 165°F.
In the final 2-3 minutes of cooking, brush the skewers generously with the mango glaze, turning occasionally to caramelize all sides.
Remove skewers from grill and let rest for 3-5 minutes. Brush with additional mango glaze before serving.