Place potatoes and green beans into a large pot. Pour enough water over potatoes and green beans just to cover and season with salt and pepper; bring to a boil. Reduce heat to medium-low and simmer until potatoes are tender, about 20 minutes.
Place bacon in a large skillet; cook and stir over medium-high heat until evenly browned, about 10 minutes. Stir flour into bacon until flour forms a paste, 2 to 3 minutes. Mix bacon mixture into potato mixture; bring to a boil and cook until thickened, 5 to 10 minutes. Mix vinegar and sugar into soup.