The price the insurance company pays is almost never going to be higher than what you would pay if you're uninsured. You're confusing your co-pay with the uninsured cost of a flu shot. If Sam's Club and Costco can offer flu shots for $15 [0], it's a safe bet that the cost to an insurance company is less than that.

[0] https://www.bradsdeals.com/blog/where-to-get-a-cheap-flu-sho...