Vitamin B3 deficiency (niacin) is going to be the most common reason why ducks have trouble with their legs. As well as the easiest to treat. Excellent advice has already been given. Get the liquid b complex ASAP. It has another b vitamin in it that is called “a feel good vitamin” because it literally makes you feel good. So it can only help the situation even if the deficiency isn’t the problem. If the deficiency is the problem, it can take around a week to see improvement based on the severity.
The complex is in the cattle and poultry vitamin shelf at TSC and I’d bet it’s in similar sections at a local feed store.
If you are concerned about botulism, there isn’t a whole lot you can do other than flush the toxin out and hope they make it. But the toxin is a paralytic, meaning the limbs are paralyzed first then the major organs. They eventually suffocate because their lungs are paralyzed. So it normally is fast progressing infection. It eventually wouldn’t be able to hold its head up.