I would grow the duck weed in the kiddie pool and not let the ducks in it, use it for growing. It needs nutrients, and still water. I think you would be better off just feeding it to your ducks yourself.
I have TONS of duckweed growing in my pond. It's probably 24'x40'. I don't have ducks anymore but the chickens eat it, they aren't real fond of it but they eat some. I scoop it up with a pool skimmer and feed them a half a five gallon pail every day during the summer, ponds froze over right now. They love the polly wog tadpoles, baby frogs and leaches that come with it.
I read about growing it in fish tanks and kiddie pools, that's where I realized I had a pond of it!