1. Preheat grill to medium-high heat.
2. Combine mayonnaise, 2 tablespoons vinegar, 2 teaspoons black pepper, 1/8 teaspoon salt, and lemon juice in a small bowl, stirring well. Combine 1 tablespoon vinegar, cabbage, and pickle juice in a medium bowl; toss.
3. Sprinkle chicken with 1/2 teaspoon black pepper and 1/8 teaspoon salt. Place chicken on a grill rack coated with cooking spray, and grill for 6 minutes on each side or until done. Cool; shred chicken. Combine chicken and mayonnaise mixture in a medium bowl; toss to coat. Place one flatbread on each of 4 plates; divide chicken mixture evenly among flatbreads. Top each serving with about 1/4 cup cabbage mixture and 1 pickle; roll up. Cut each wrap in half diagonally.