It's nice to believe this, but having a flu jab is only proven to protect yourself. It's not sterilising immunity so you can still become infected, shed virus, and infect others while asymptomatic.

It's quite dangerous if a lot people don't get that the covid vaccines also aren't proved (and are unlikely) to contain transmission. Risk is folks think that we will not longer need to care about hygiene, masks, isolation, quarantine and tracing once most people have been vaccinated.