Yes, mine is covered by insurance. DH's insurance (high ded) doesn't cover it. But City Market had a $15 off flu shots you could load to your value card so it only cost him $10. It pays to shop around.
I got a flue shot for the first time about 10 years ago. I ended up getting so sick that I couldn't even move off of the couch for a week. I have never been so sick in my life. I haven't got the flu shot since, and haven't been sick since. No flu shots for me!!