You should check around, bunch of groups / counties provide them for free or low cost. Also Costco was at least a few years ago dirt cheap without a prescription.
For some reason CVS refuses to take my UnitedHealth insurance for flu (but will no problem for covid). They said it would have been 200 bucks and I laughed at them and went to Costco.
I'm an EMT w/ a fire dept, we run a local flu shot drive for our community for free. Check for other resources like this for example in your community, or perhaps at the county level.