Preheat a grill to medium high and brush the grates with vegetable oil. Toss the chicken with the olive oil, vinegar, rosemary, garlic, red pepper flakes and salt in a large bowl. Place a cheese cube on a piece of chicken and wrap tightly with a slice of prosciutto. Repeat with the remaining cheese, chicken and prosciutto.
Thread the chicken bundles onto eight 10-inch skewers along with the tomatoes. Grill the kebabs, covered, turning occasionally, until the prosciutto is crisp and the chicken is cooked through, about 10 minutes.