We don't really stockpile flu vaccines because influenza changes and so older versions would not be very helpful. Instead we stockpile the raw materials and production capabilities for the vaccines. The traditional flu vaccine is made using chicken eggs infected with the virus so many countries have their own emergency supplies of chickens/eggs for this purpose.

Now that we also havecell based flu vaccines that don't require chicken eggs as well as future mRNA based flu vaccines that can be rapidly mass produced there will likely be a variety of of options for stockpiling/emergency preparation.