Hi.
Of course. You are learning as you go...!
Well... yes : every food grade Diatomaceous Earth will kill roundworms and are safe for ducks.
It will even feed the ground...!
Just... be careful to put a mask when using DE - really just in case.
And use it in your yard a sunny day (or at least when you know it is not going to rain), so it is 100% effective in killing roundworms!
I would not recommend it, for several reasons - one of them being it could be illegal to use bleach in your yard. (?)
I also would not use chemical products when efficient natural ones exist, and are at least as effective as them.
And if your ducks eat the insects/slugs/grass sprayed with food grade DE, they at least won't be hurt by it (at the contrary)!
You are not lucky... and you are not at fault.
Even wild birds could be the cause of an infestation...
There is nothing you could do to prevent it... in your ground at least!
Indeed : in my experiences with chickens (my ducks have never had worms, so I can not tell), if you regularly feed food grade DE to your birds and/or put Apple Cider Vinegar in their water, they should not get infested by worms or whatever parasites...!
(Besides, DE is good for them. So you don't lose anything by trying it, right...?)
From what I have found by searching on the internet - just now, because I had never heard about "distilled vinegar" before... yes : "distilled vinegar" should be okay to use!
...Good luck!