Stir the flour and 1/4 cup of the milk together in a saucepan until no lumps remain. Stir in the remaining milk and sour cream. Bring to a simmer over medium-high heat, then reduce heat to medium-low, and simmer for 15 minutes.
Add the green beans, and cook until tender, about 5 minutes. Stir in the vinegar, and season to taste with salt before serving.