Dee's Duck...
Re your current situation...
I have just Incubated my first Duck Eggs, and found that, after hatching :
Ducklings need warmth, more so than what a heat lamp or brooder can give.
Especially when you have a little one, or one that is not as strong. So apart from just putting them back in the incubator, brooder, or under a wayward Mum, (Mom) warmth and safety are the best medicine.
Any mammal, and birds here, need primarily warmth, then fluids and latterly food, to turn the corner. And back to thriving again.
Remember, when your are Sick, or Icky etc, you want a Duvet Day (warmth) a hot honey / lemon drink (fluids) and when you can rejoin the human race (unless it's manFlu

) some of your Grannies recipe of homemade chicken soup (food.)
With my weak and overdue Runner Duck Eggs and associated Ducklings, they were given a tiny "warm water" bottle to each side of them... I used those '100ml / 8oz' travel sized fluid / lotion bottles.
I tested them on my wrist, like what you do re baby formula bottles.
And gave them tiny drops of warm water with a dot of honey (or sugar) from dipping my finger in the fluid, and placing my finger tip on the side of the beak... And, back into the Incubator, or under that heat lamp, >> with a warm water bottle, & a soft fibre item. <<
This gives, 1st : warmth, 2nd : comfort.
If they need to be removed from siblings, or are solo Hatcher's, a fluffy fibre cloth, or soft toy, really helps.
You can prop up the patients head and chest, so they can still breathe, but not so that their head or body is not just flat on the floor. And being cuddled by a non shedding fabric 'nest' keeps them safe, even if they are flat out with exhaustion, and deep post hatching sleep.

(Propping up improves their circulation and associated recovery.)
Done many a time with Marans Chicks, that struggled in their first few days.

: Giving fluids
Dropper or syringe feeding only gets aspirated, and results in snuffling, and or choking, and, I'm afraid respiratory demise. (I always use my finger tip.)
They just get a cold, don't keep their appetite, and associated temperature, and I'm afraid, fail fast.
: Helping your hatchlings.

Warmth, warmth,warmth, fluid, then food. Is the way to go.
Direct contact with a warm object [Body temperature : Only !]
.... Will do more good than, any hairdryers, near direct dry heat etc. And a fluid with added sugary elements, will improve the energy levels of said newbie chick or duckling.
And keeping the fluffy patient, moving, eg : gently stroke them, move the little thing, gently in your cupped hands, etc, will keep the circulation going.
Even at one time, I needed to blow my breathe over and above, the infant from a little distance, to keep it going.
ABC (Airways/Breathing/Circulation) applies to many living, but struggling things, over and above that of ill folk !
Hope this prescription helps *...
... QKR: MD Dr.Duckling
* Only my recommendation, I'm not a Vet, but looked after those like us.
I'm so new to ducks and ducklings, my Daisy is only two weeks old...*
* However, I learnt a lot, trying to keep her tiny tot sibling alive, with a serious non absorbed egg yolk issue, for five days, alas so tiny, she passed away after 5 days. But know what I did with Daisy Duckling worked...