So there aren't any natural ways to worm ducks or chickens?
Well, it's natural for the birds to have some degree of internal parasites. It's UNnatural for them to be free of worms completely. So, technically, no, no such thing as "natural" dewormers.
People used tobacco for ages to get rid of intestinal worms - it even works to some degree. But tobacco is toxic to the birds as well as worms. Also, in the USA, it's not legal to use or feed cancer-causing substances on meat (or egg, or milk) animals. (Plus, not smart, even if you weren't selling the meat or eggs commercially.) Most other traditional dewormers also have some sort of negative side effect.
DE has been tried for ages - in trials, it doesn't work. Some people still use it. It doesn't seem to hurt the animals.
As for plants with effects on worms, if you check out this link:
http://www.scsrpc.org/ they have pages addressing specific plants which have been found effective for specific worms in goats & sheep. I don't know if these plants would have the same effect on ducks, etc, but it is a place to start.
As always with animal health - good hygeine is the place to start.