I'm very sorry to hear your duck has been having leg problems for such a long time with no improvement. Ducks, specifically Pekins, and other heavyweight breeds are often prone to developing leg-related problems, whether that be Bumblefoot, arthritis, sprains, strains, deficiencies, they tend to get the most of it. Risks of leg problems can be increased by keeping such breeds in hard compacted grounds that offers little support to their legs, not allowed to swim in deep water to relive weight off their legs, and fed diets intended for other poultry such as chick starters which tend to contain little niacin content in their feed, which can increase the chances of leg-related problems.
Taking the time to look at your setup, housing, feed, etc, and what might make it more likely for the duck to come down with such leg problems is just as important as treating the problem itself.
Of, course, for now, we're going to be a little over precautious of what we keep him on since he has a current leg problem. You'll want him on a soft padded area, with feed and water provided in a deep dish to allow proper cleaning of the nares. He should be allowed to bath in cool water a few times a day, possibly with Epsom salts added every few days to help reduce swelling of the leg. Regardless of what he's being fed, starting him on a niacin supplement such as B complex, may help with the ongoing problem by increasing leg strength, structure, and health.
Just looking from the pictures, and the info you provided I can't immediately tell you why his leg has been swollen for this long. Your vet likely has a better idea than me. Since it is warm, swollen, and hasn't resolved itself very much, I would be inclined to think of infection of sorts, possibly osteomyelitis. One common bacteria that is often found on the dermal surfaces of birds skin, and what I usually end up culturing from their wounds, is staphylococcus aureus. Such a prevalent cause of bacterial infections, it's widely known for it's resistance to several antibiotics classes, cillins, such as Amoxicillin. Clavamox is basically amoxicillin with clavulanic acid, and because of the addition of clavulanic acid it had good effects against staph. . The problem is the last few years there has been a great increase in the amount of methicillin-resistant staph, which is resistant to both amoxicillin, and clavulanic acid/Clavamox.
Therefore there is a possibility the "infection" he has is resistant to the Clavamox you're using currently. It would be my suggestion, to combo a quinolone class of antibiotics with the Clavamox such as Enrofloxacin, or Ciprofloxacin. Both being quite effective antibiotics that are used in conjunction sometimes with Clavamox for even more coverage/effectiveness.
You can obtain Enrofloxacin online, the dose being 0.05ml per pound twice daily, for no more than five days. It may be worth trying that for a little while since the Clavamox is not working.
You can find Baytril (Enrofloxacin here) :
https://allbirdproducts.com/products/baytril-10
Baytril is such a fast-acting antibiotic, you'll know if it works after just a few days.
If you get her on the Baytril, and it doesn't work, you can get back to us, but I feel the chance of infection hasn't totally been ruled out yet, and starting her on Baytril should rule out a bacterial infection.
