Heat a large soup kettle over medium-high heat. Add kimchi, sesame oil, soy sauce, and vinegar, followed by the hot water and rice. Just as the soup comes to a simmer, add tofu, breaking it up with your hands as you drop it in the pot. Return to a simmer. Stir in scallions and serve immediately, letting everyone flavor their soup with extra sesame oil, soy sauce, and vinegar to taste.