Mix the oil, garlic, basil, oregano, lemon zest, salt, pepper and pepper flakes in a large bowl.
Take 2 Tbsp of the oil mixture and place into another bowl and set aside.
Prick the chicken breasts with a fork all over on each side. Cut into 1 1/4 inch chunks. Add to large (first) bowl of marinade. Refrigerate and marinate for at least 30 minutes and no longer than 3 hours.
Whisk together mayo, vinegar and lemon juice with the 2 Tbsp of oil mixture set aside earlier.
Remove the chicken and thread onto metal skewers.
Heat your gril for 10 minutes on high.
Clean and oil your cooking grate. Place the skewers on the grill, turning frequently. Cook for 10-15 mintues.
Remove from grill and allow chicken to rest for at least 5 minutes.
Grill the rolls on grill for a few seconds each. Remove quickly or they will burn.
Remove the chicken from the skewers directly on the rolls. Drizzle with mayo sauce mixture.