Corona viruses are slow to mutate in general, and flu is especially fast.

That's why you need a new flu vaccine every year - every year a lot of time is (was?) invested in tracking what flu mutations are appearing and trying to predict which ones will be the main ones next year. Once they've determined what they think are most likely, the vaccines are developed for those. Happily flu mutations mostly impact the protein structures sticking out of the virus wall (the HxNy is an actual description of these proteins, hemagglutinin and neuraminidase), so it's mostly a matter of retargeting an existing set of vaccines rather than creating a whole new vaccine from scratch.