Hi, Apix, and welcome to BYC!
First of all, you should take a look at this thread-->
https://www.backyardchickens.com/t/742668/pekin-duck-club/6950 starting on page 696 and post #6952 by @jannakaye . You would want to read her post and the responses to it, though there are unrelated things mixed in that you can skip over.
While you don't have the same issue that jannakaye had, the suggestions I gave her about nutrition in post #6966 apply in your situation as well, but for a different reason. The issue with your drake's bill doesn't look nutritional, or at least not strictly nutritional. It is almost certainly environmental, and I suspect it's caused by swimming in a pool intended for humans. I say that because of the distribution of the severe dryness and peeling from the base of the bill and pretty evenly distributed around the nares (nostrils). That means the drake is sucking in something and blowing it back out, and that is causing the irritation. That something is probably human pool water that has chlorine and other chemicals in it. Pool chemicals will dry even human skin.
While the dryness itself isn't life-threatening, the severity of that peeling could lead to infection. Similar to what I put in that post for jannakaye, I would wash his bill off with a soft cloth and some wound wash like Vetericyn Wound and Skin Care, then put a thin film of Neosporin without pain reliever on it. It would be best to apply the Neosporin with a qtip so you can kind of paint it over the whole bill and still avoid getting it in his nares. I would do this twice a day if he'll tolerate it, at least once if not. I would not under any circumstances let him back in that pool. If you want to let him in for a few minutes as a once per week treat later on, I doubt that would do any harm, but not until his bill is completely healed.
Are you able to provide him some clean, fresh swimming water other than your pool, maybe by picking up a kiddie pool he can splash around in?
