Ducks have webbed feet because a gene that is already expressed in this area has extended its expression domain (or chickens lost it, depending who was first, the chicken or the duck).
In this case gremlin, a BMP inhibitor, is expressed in the interdigital space (the space between your toes) in ducks, but not in chickens. This prevents the apoptosis (regulated cell death) of the cells between the digits. Hence the duck never loses the tissue between its toes.
You can similate this by putting a bead loaded with gremlin protein inthe interdigital space of the foot of a chicken embryo. This mimicks the effect of gremlin in the duck. There is no apoptosis and you end up with a chicken with webbing between the digits where the bead was placed.
The question then becomes how this expression pattern was changed, and although we do not know exactly, developmental biology has the theories to explain this. Which are tested and proven in other systems.
in conclusion, there is no specific gene for webbed feet. We are dealing with a slight alteration of an existing system, with rather beneficial consequences if you are fond of a pond.
and of course, this cannot be measure in terms of gene frequency. This is on the level of combinatorial control of gene expression.