Gill flukes are not very common among small fry of any domestic discus.
Based on my experience and your description, i suspect you are not keeping their water clean enough and may be having troubles caused by poorly or incompletely cycled filters. Discus fry are very sensitive to poor water quality and act like or experience high losses unless the water quality is improved.
You need to be sure that you feed them frequently but no more than they can eat in a few minutes. If you are feeding them Artemia nauplii, be sure you vacuum up any left over dead brine shrimp as soon as it's practical.
One way to help maintain good water quality other than frequent water changes and good hygiene is to use a canister filter. Equip the filter inlet with a prefilter and add a ball valve to the return line if you don't have built-in valves so you can reduce the filter return flow rates low during their first 7-10 of free swimming. I would also include a sponge filter.
Exactly when do your problems with the fry become evident and has the rearing tank been set up long enough for the filter(s) to become cycled.