While the problem certainly appears to have originated from the pet shop where you got the fish, on the surface it doesn't sound like fin rot, as suggested in your thread title. Fin rot is a bacterial development that causes fins to begin being eating away, and fin tips will often be white, but a white slime coating is not normally cited as a fin rot symptom.
In any event, frequent, large wcs, along with improvements to water quality & conditions, by thorough vacuuming of the substrate, and a good tank cleansing routine should improve the situation.
The fact that you have some ammonia, and nitrates of 40 ppm is not a good sign. Discus do not do well with nitrates above 10 ppm (they should preferably be under 5 ppm), so wcs should improve this condition (does your tap water contain nitrates ?)
Perhaps someone knowledgeable at the store can confirm whether or not it is fin rot, and a pic of your tank would certainly shed some light on the matter.
White slime on the fishes' bodies may be a loss of slime coatings, particularly in the discus, and taking the above-mentioned actions should help to improve that condition as well - which could also have a bacterial origin.
If it is in fact fin rot, treatment should be given using methylene blue, or malachite green, or an antibiotic like tetracycline.
Please post a pic so we can help determine your situation.