Fry the bacon until crisp. Remove with a perforated spoon and reserve. Remove the tough outer leaves and hard core of the cabbage and chop into medium-fine shreds. Add the cabbage to the bacon fat and fry over medium heat, stirring occasionally until the cabbage is tender and brown-flecked in about fifteen minutes.
Stir the flour, sugar, and salt into the cooked cabbage. Mix the milk and vinegar and stir it into the cabbage. Stir constantly over medium heat until thick and smooth. Sprinkle with bacon bits and serve hot.