Answer: No
"Stomach flu" is just a nickname for viral gastroenteritis. It is not related to influenza, the real flu. Your annual flu shot will not protect you from the stomach flu. The stomach flu is really viral gastroenteritis. The viruses that cause the stomach flu are not related to the influenza virus that causes the real flu. The real flu can sometimes cause a person to vomit, though. My 2 year old vomited a few times when he was sick with influezna A in March 2013. (Yes, he still got influenza A even though he had the flu mist vaccine.)
It is very important to clean with a product that actually kills norovirus when a stomach bug is in your home such as the Clorox® Hydrogen Peroxide Spray
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--Annie Pryor, Ph.D.