Classicly the The flu is characterized by a collection of symptoms that can often occur suddenly, including:

Fever (higher than 100° F)
A fever occurs when your body temperature increases in response to illness or injury. Your temperature is considered elevated when it is higher than 100°F.

Chills
Body chills that are not related to a cold environment can be a sign of the flu.

Headache
A headache associated with the flu may appear suddenly, and be related to body aches or nasal congestion you're experiencing.

Extreme tiredness
It's normal to feel tired at the end of a long day or when you don't get adequate sleep, but unexplained tiredness can be a sign of the flu.

Dry cough
Know your cough. A productive cough (coughing up mucus) is common with a cold, while a non-productive or dry cough (with no mucus) is associated with the flu.

Sore throat
Swelling in the throat can lead to a sore throat.

Runny nose
Runny nose may also occur but is more common in children than adults.

Muscle aches
While it is normal to feel body aches from physical overexertion, body aches that are sudden and unexplained can be a sign of the flu.

Stomach symptoms
Stomach symptoms such as nausea, vomiting and diarrhea are more common in children than in adults

Chest discomfort
Chest discomfort is often severe with the flu.

Doctors of the period ran the gambit as far as their expertise went. It actuality the Civil War was one of the first attempts to "standardise" medicine. For one example the giving of tests to doctors to see if they were "qualified" to be a military doctor.

The fact that they had so many different classification of Illness which included a "fever", but did not seem to have one which fit the symptoms we now classically associate with the Flu tells me that they probably misdiagnosised these symptoms as something else.

The problem with a Coryza diagnosis is that it was associated with an Inflamation caused by an allergy or a common cold. And as you will read in the classic symptoms of the Flu there is a difference between the Common Cold and Influenza. Particularly the production, or non production, of mucus in the cough.

Of the symptoms that would have been of most concern to the CW doctor would have been the High Fever, Stomach and Chest complaints. These would have been the symptoms that they would have treated. It is my 'Guess' that "Camp Fever" or "Bilious Remittent Fever" would have been the catch-all diagnosis that would cover for these symptoms.

Of course this is all personal opinion and without more clear medical diagonsis of diseases of the period it is going to be near impossible to prove beyond a reasonable doubt.