Bake dinner rolls as directed on package. Heat gas or charcoal grill. To flatten each chicken breast, place chicken between 2 pieces of plastic wrap or waxed paper. Working from center, gently pound chicken with flat side of meat mallet or rolling pin until about 1/2 inch thick. Sprinkle chicken with salt and pepper.
When grill is heated, place chicken on gas grill over medium heat or on charcoal grill over medium coals; cover grill. Cook 6 to 8 minutes, turning once, until juice of chicken is clear when center of thickest part is cut (170°F). Slice each chicken breast in half crosswise. Slice each piece of cheese in half; top each chicken breast piece with slice of cheese; cook 1 minute longer or until cheese is melted.
In small bowl, mix peach preserves and pepper flakes. Slice rolls; place chicken on bottom halves of rolls. Top each with 1 tablespoon preserves mixture. Cover with top halves of rolls.