This is a very interesting question because it also deals with the limits of veganism.
I could not find any reference to an existing vegan vaccine and I think it is very unlikely that one exists.
This is by design because it is a biologic product:
A vaccine typically contains an agent that resembles a disease-causing
microorganism and is often made from weakened or killed forms of the
microbe, its toxins, or one of its surface proteins
From a biochemical perspective this is a very complex cocktail and even if it would be feasible it would be much more expensive to produce an effective vaccine without involving animal products.
The broader picture
When you say vegan flu, it is also important to understand what "vegan" means. This article explains why being vegan and getting vaccination is possible if using a more practical definition of being vegan:
Veganism is a way of living which seeks to exclude, as far as is
possible and practicable, all forms of exploitation of, and cruelty
to, animals for food, clothing or any other purpose.
The same article provides a real-life example about the limits of veganism:
However, vaccines fall under the broad umbrella of medicine. Many/most
vegans view medicine separate to veganism. If you go to A&E after
falling off a roof, you’re not going to deny pain relief that may have
animal derived ingredients or be treated by a surgeon who may have
practiced on animals. It is neither possible nor practicable to
withhold necessary medical treatment.
Also, it is important to understand that in the specific case of (some) vaccines, the herd immunity plays an important role:
(..) if large amounts of vegans started denying vaccines? Not only
would groups of unvaccinated people being together be extremely
dangerous to them, it would also allow diseases to spread beyond these
Clearly helping spreading a potentially deadly disease is not in sync with being vegan (from a biological perspective humans are animals too).
In the specific case of flu, getting a vaccination might not be really necessary unless you are in one of the risk categories (e.g. children, seniors), but keep in mind that the flu is a contributor to death, even if it’s not the main cause