They make special plyers just for this but those nails are going to be ring shank nails and are going to leave craters when there pulled.
There called Tower Pincers for some reason. Lowes and HD both them in the tool dept.
If the plan was to save the flooring, this almost never works out. There's all most always a reason someone covered it up in the first place, stains, insect damage, coming loose, ect.