Bring cabbage, bacon, 2 cups water, and vinegar to a boil in a large saucepan over medium-high heat. Reduce heat to low and simmer uncovered until cabbage is very tender, about 3 hours, adding more water as needed.
Whisk remaining 1/4 cup water and flour together in a small bowl and gradually add to cabbage mixture. Continue to simmer until thickened, about 5 minutes more. Season with salt and pepper.