Mix kimchi and onion together in a large bowl; add flour and mix well for 1 minute. Pour water over kimchi mixture and stir until batter is evenly combined.

Heat a skillet over medium heat; add about 1 teaspoon vegetable oil. Scoop about 1/4 cup batter into the hot skillet, creating a pancake that is 1/4-inch thick; flatten and smooth the edges using a spatula. Cook pancake for 3 minutes; flip, pressing lightly, and cook for 2 minutes more. Repeat with remaining vegetable oil and batter.

Whisk green onion, soy sauce, sesame seeds, red pepper powder, and sesame oil together in a bowl; serve alongside pancake.