The smallest angle will vary with the height of the knife blade above the vise.
I have a chef’s knife that sticks above the vise by 1.75 inches when I clamp it and I can manage nearly 13 degrees per side on its edge without scraping the vise jaws. Very shortly though, a new attachment will become available that will allow angles much less than 15 degrees per side and approaching zero degrees.Look for it later this winter or early spring if I am not mistaken. Clay please correct me if I am wrong here.
Leo