Welcome to BYC.
How does the leg feel - is it hot, swollen, is there redness?
Can you gently bend the joints without hearing or clicking?
Could you post a video of the duckling trying to walk on its feet?
If you can isolate the injury to a soft tissue injury (sprain/strains) to ensure you're not dealing with a dislocated, or broken bone, treatment will be fairly straightforward.
When dealing with leg injuries, one should address all factors that predispose, or may in future cases predisposes the bird to develop the injury.
Environmentally all things should be altered to hasten the healing of the injury.
This would include padding the substrate for the bird, ensuring the other ducklings arent pecking at it's leg, and eliminating any objects it may be getting its legs/feet caught on, etc.
Obviously, these injuries can be quite stressful for the bird, so consider adding a poultry vitamin to its water/feed/ or treats every few days to help correct any nutrient and electrolyte deficits.
Bathing in water is okay, but the duckling should be placed in warm (not hot) water and placed directly into a warm environment afterward. Time, and rest will ultimately be the best treatment in the long run.
I hope you see some improvement soon.