They have to go through the same process as anything else. For a seasonal vaccine like the flu, there's an addendum that gets filed to your BLA describing the changes. If an inactivated pathogen is used, a small clinical trial is required each time to demonstrate that the inactivation is working properly. The annual flu shot doesn't have to go through a whole new round of Phase 1, Phase 2, and Phase 3 clinical trials every single year when they slightly tweak the formula. It never has.
But you're right about generation 1 and 2 vaccines being too slow. That's why the flu vaccine is usually only 40-60% effective: it takes months to make and Influenza rapidly mutates. The mRNA platform lends itself to very rapid change because nothing needs to be grown ("cultured"). You simply plug in the nucleotide sequence for the antigens you want and start mass producing. They'll have to do clinical trials for the first mRNA flu vaccine products to get the BLA. Subsequent ones will go very quickly, which means they can wait until we see what flu strains actually hit the US to create a vaccine that targets them. I wouldn't be surprised to see >90% effective flu vaccines once they're available on the mRNA platform for a couple years.
That's great news as it'll save tens of thousands of American lives each year.
Flu shots are useless. Never get them I’m I’m just fine. More than likely they make people sick and die. Big Pharma will cease to exist without sick people.