Mix vinegar, soy sauce, 1 teaspoon garlic paste, ginger paste, salt, and pepper together in a shallow dish. Add chicken breasts; turn to coat. Marinate in the refrigerator for at least 30 minutes.
Heat 2 inches oil in a heavy pot to 325 degrees F (165 degrees C). Fry potatoes in batches until golden brown, about 5 minutes. Transfer to paper towels to drain.
Heat 1 tablespoon vegetable oil in a large skillet over medium heat. Remove chicken breasts from the marinade and cook until browned and no longer pink in the center, 6 to 8 minutes per side. Transfer to a cutting board; slice into thin strips.
Mix remaining 1 teaspoon garlic paste with mayonnaise in a bowl.
Spread garlic mayonnaise inside pita breads. Fill each pita with French fries, chicken slices, and pickles.