Some people have success with rubber livestock loafing mats - they clean up with a hosing and can be changed out. You might have to regularly pull them out to clean under them, though.
Concrete can abrade duck feet, and in that environment, the ducks are at a higher risk of bumblefoot, an infection that begins as a bump on the foot but can become systemic and fatal. Early treatment twice a day with triple antibiotic works for us - no drama other than holding the duck for a minute.
I wonder if you could put planters just inside the perimeter of the fenced area on top of the concrete for some vegetation and a place to noodle the soil.
For a quick fix, if it were me, I'd try putting a combination of sawdust, straw, dry oak leaves, a sprinkling of peat moss, and maybe a little coir (some caution about salinity, so consider that) all about three or four inches thick on top of the concrete while I looked for a more long term solution. It will protect the ducks' feet, absorb odors and moisture, and give the ducks something to noodle with. The nice thing about this approach is that you would just periodically scrape the material off the concrete once it reached saturation, then add it to a compost pile to supercharge the compost. Or you could just layer it in a future garden bed and let it compost in place. That material is wonderful for plants!
If the concrete is flat, that's going to make drainage nonexistent or at least very slow, so I would really lean toward having something high carbon and absorbent on the surface.
Keep us posted!
