Place the cubed chicken in a large zip-top bag.
Add the lemon zest, lemon juice (from the 3 lemons), minced garlic, rosemary sprigs, olive oil, Kosher salt and red pepper flakes to the bag.
Seal the bag and turn it several times to thoroughly coat the chicken with the marinade; refrigerate and marinate for at least 1 hour and up to 2 hours.
Remove the chicken from the marinade and discard excess marinade.
Thread the chicken cubes onto 4-inch skewers, adding a couple of lemon wedges to each skewer as you go.
Preheat the grill to medium heat. Place skewers directly over the heat and grill 6 to 8 minutes, turning occasionally for even cooking, until the chicken is cooked through.
Transfer cooked skewers to a platter and let rest briefly; squeeze the grilled lemon wedges over individual servings before serving.