I believe that the problem here is that the combination of symptoms, which became Identified as the "Spanish Flu" of WW I, during the War Between the States would have been treated as individual symptoms. The most prominate of which would have been the high fever and the bodyache, and the developement of Pneumonia.
They probably would have treated it with one, or a combination of the herbal remedies for Fever such as Triosteum perfoliatum, otherwise known as "Fever Root", Liriodendron tulipifera, otherwise known as the Tulip tree, or Eupatorium Perfoliatum, also know as "Boneset".
Each of these herbs were common in the regimental medical chest of the period and were Diaphoretic in nature which caused the body to sweat and therefore reduce a fever.
That would be my understanding of the situation.