Oh, sad to read your KC is having trouble.
The swollen joint could be a few things. The leg needs to be checked for any injury (in one case, an old leg band had not been removed . . . but it was so far up the leg it had not been seen). Baths in lukewarm water deep enough to swim in, preferably three times a day, but I understand it may not be possible. The idea is to get weight off the foot, improve circulation and strengthen muscles and relax the leg.
Check out the foot. Are there any bumps with dark centers on the bottom? Ducks have callouses that are fine, but a bumble is puffier.
If there is no bumble on the foot, you may be dealing with a different kind of leg injury. You could try triple antibiotic on the foot and leg for several days to see if there is improvement. In a perfect world, you would be able to get the duck to a vet for a good diagnosis. If that is not the case, you need to make your best guess. I am told that the oat doctors take involves the idea, "first, do no harm."
Something else that can help sometimes is an Epsom salts compress. Es is a laxative so you don't want the duck eating it or drinking Es water. So I put a few tablespoons of Epsom salts in a shallow dish (unbreakable is good) with a quarter cup of warm water. I get a very clean rag or some paper towels. I get my beloved to hold the duck, and I wrap the rag or paper towels around the foot and leg and we all sit there together as long as we can stand it, somewhere between three and five minutes.
I did this twice a day when Romy was recovering from an infection caused by a splinter. She was pretty good about it once she discovered I was serious.
Epsom salts is a very good thing to have on hand and does not cost that much, if I recall correctly.