Quoting Squeaky McGee:" Sounds more like a GI bug to me. Influenza is a respiratory bug, not a GI bug, contrary to popular belief. ... [snip!] ... old is he? Try your best to keep him hydrated. Pedialyte (or watered down Gatorade) will help keep his electrolytes in check."
OP, I hope every one makes it through this quickly. Defintely work on hydration, but only tiny bits of liquid at once. If you rush or overdo the liquids, it will just come back up.
Plenty of influenza strains have gastrointestinal symptoms as well as the respiratory issues. I was hospitalized for the influenza a couple of years ago and while the sore throat, fever aches and so on started first, I vomited everything that went in orally.