Preheat the broiler. Soak 8 long wooden skewers in water, 15 minutes. Line a baking sheet with foil and brush lightly with vegetable oil.
Meanwhile, whisk the ketchup, soy sauce, vinegar and honey in a medium bowl. Transfer half of the sauce to a separate bowl and set aside for dipping. Toss the chicken, water chestnuts, pineapple, bell pepper and 1 tablespoon vegetable oil in a large bowl; sprinkle with 1/2 teaspoon salt and a few grinds of pepper. Thread onto the skewers, alternating the ingredients. Transfer to the prepared baking sheet.
Brush the kebabs with some of the remaining sauce and broil until they start browning, about 4 minutes; flip, brush with more sauce and continue broiling until the chicken is golden and cooked through, about 3 more minutes. Serve with the reserved sauce and rolls.