Preheat oven to 200 C / 400 F. Line a large baking tray with baking paper.
Place chicken in a bowl. Add shawarma spice mix, olive oil and lemon juice. Season with salt. Toss to coat chicken in the spices. Marinate in the refrigerator for at least an hour or overnight.
Arrange chicken on a baking tray in a single layer. Bake for about 40 minutes or until chicken is cooked through. Turn on the grill. Grill for about 5 minutes. Remove from grill. Rest for 10 minutes. Slice chicken as thin as possible. Set aside.
To make garlic sauce, combine together mayonnaise, minced garlic, lemon juice and red pepper (chili) flakes in a bowl. Set aside.
To assemble, spread 2 tablespoons garlic sauce on pita bread. Top with chicken, cucumbers, lettuce and tomatoes. Roll into a tight wrap and serve.