My daughter had some sort of bizarre flu bug last week. Within less than 24 hours she became severely dehydrated -- even though she only vomited twice and had no other symptoms except malaise, a sore throat and cough and a headache. She just couldn't bring herself to drink.
I ended up coming home from the Night from Hell working as a pediatric nurse, dropped into bed for an hour, only to be awakened by my 14 year old crying in pain that her belly hurt. (She's a total stoic so this is very unlike her). She looked awful, clearly very "dry". So back to the hospital we went, with me totally bleary eyed, my husband driving because I was in such bad shape. They gave her two bags of Fluid and some phenergan and the difference was phenomenal. She came home with a scrip for more, and only had to take two over that day, then she was fine. (Now I think I'm coming down with it so I'm being very careful to drink a LOT).
That phenergan stuff is magic. I highly recommend keeping it onhand. But I'm not sure if it would help with the vomiting from coughing, though. I have a lot of experience -- unfortunately -- with coughing that hard because of my Sarcoidosis. In fact, that probably happens to me a couple times a month. I think the key with that is getting the *cough* under control.
And yes, true influenza doesn't usually involve the stomach. "Stomach flus" are more often some sort of intestinal virus or food poisoning, which is a whole other thing. OTOH, you can become so dehydrated from influenza that it can throw your electrolytes off to the point where you become nauseous; I think that's what happened to my daughter. It's a vicious cycle at that point because you need to drink, but can't because you're nauseous, which makes it worse. The only real way to get around that is getting fluids in SOMEHOW. IV fluids are probably the best way. I've treated a few kids who came in vomiting whose nausea went away just from the fluids; we didn't even have to use phenergan. Weird, I know, but that's the human body for ya.