In a medium bowl, mix flour, eggs and oil with 11/2 cups water until a smooth batter is formed. Stir scallion greens, chives, carrots, squash and shrimp, if using, into batter.
Place an 8- inch nonstick skillet over medium-high heat, then coat bottom with oil. Ladle in about a quarter of the batter and spread it out evenly into a circle; if first pancake is too thick to spread easily, add a little water to batter for remaining pancakes. Turn heat to medium and cook until bottom is browned, about 3 minutes, then flip and cook for another 2 minutes. Repeat with remaining batter.
As pancakes finish, remove them, and, if necessary, drain on paper towels. In a small bowl, mix together the vinegar, soy sauce and sugar. Cut pancakes into small triangles and serve with dipping sauce.