Visitors insurance is meant to cover any new, unexpected sicknesses and injuries. So, if you were to become sick with the flu after your insurance's effective date, treatment for the flu would be covered by your insurance. However, flu shots and any other immunizations / vaccinations are not covered by travel medical insurance. There are currently no short-term health insurance plans that will cover the cost of vaccinations.
If you must have a flu shot while in the US, you may obtain one at most of your local pharmacies (Walgreens, Target, Walmart, etc.) Flu shots generally cost $15-$30.
For more information on visitors insurance and preventative care, see: Routine Care and Travel Medical Insurance
To purchase insurance to cover you for any unexpected emergencies on the remainder of your trip, you may view your options and get a personalized quote, here: Visitors Insurance
Insurance rates are regulated by law. You can't find the same insurance plan for a lower price anywhere else