H5N1 is concerning. It's made the jump to mammals, but not easy mammal-to-mammal infectivity (so far as we know - although one person has come down with it, and it appears that was from contact with dairy cows that had been infected. This particular variant seems to be both infecting bird species that don't normally contract it (e.g. raptors) and the 'reservoir' species (migratory waterfowl) are showing signs of illness.
One challenge is vaccine effectiveness; a H5N1 vaccination doesn't produce the same level of immune system response as the seasonal variants - so there'd need to be more material injected or along with an 'adjuvant' (essentially something to get the immune system 'pissed off' and mount a stronger response). On top of that, our immune systems would be 'naive' (never exposed to something close) so we'd need two doses, one to prime, the second for a response.
That challenge leads directly into another: it seems we won't have nearly enough vaccine for everyone, particularly if your definition of 'everyone' includes the poorer countries that had to wait for Covid19 vaccine. It's not clear whether advances in mRNA vaccine production could be used for influenza - although there's at least one group that's been working on a 'universal' flu vaccine using mRNA tech - and from looking at clinicaltrials.gov there doesn't seem to be anything in the 'approval pipeline'. It's also not clear there'd be enough adjuvant (without getting into the interesting work going on using rapamycin and 'rapalogs' as adjuvants).
Bright side: influenza viruses are transmitted via droplets, so masks and 6 foot separations will probably be effective, as will hand-washing - and there's plenty of PPE. Also, this seems to be mostly happening in non-authoritarian countries, making a cover up / news blackout less likely if it starts to get out of hand (IMO, the major reason Covid19 turned into a global pandemic).
Sorry to be 'chicken little' here...