1. In a food processor, finely pulse the shrimp, scallions and water chestnuts. Transfer to a small bowl and fold in the egg white, carrot, ginger, sesame oil, rice wine and salt.
2. Lightly dust a baking sheet with flour and have ready a small cup of water. Place less than 1 tablespoon of filling in the center of each wonton. Brush one edge of wonton wrapper with water; fold over filling and pinch edges to seal. Place dumplings seam side up on baking sheet; press to flatten.
3. Stir together the soy sauce, vinegar and chili oil in a bowl.
4. Bring two large pots of water to a boil; add dumplings one at a time to the boiling water. Stir occasionally until cooked through, about 8 minutes. Transfer dumplings to a platter. Serve with the dipping sauce.