Transmissibility
Influenza viruses are a lot less transmissible than Covid-19. Public health measures targeting Covid-19, including widespread mask wearing, were effective enough to cancel "flu season" and possibly even eradicate Influenza B Yamagata. One study showed that N95/KN95 masks reduced the risk of infection with Covid-19 by 83% in real-life settings. Masks work and help you to stop worrying about your personal health.
The Basic Reproduction Number R0
The basic reproduction number R0 indicates how many infections result from one existing infection, under regular conditions without interventions like masks or vaccines. While definitions and calculations vary a bit, the differences between Covid-19 and influenza viruses are obvious. Covid-19 started with an R0 value of around 3 and has evolved towards an extremely high R0 value of about 8, making it the fourth most transmissible disease in existence after measles, chickenpox, and mumps. The R0 value of influenza, even the 2009 pandemic variant, is somewhere between 1 and 2. While human-to-human transmission has already occurred, for example in Egypt and Hong Kong, the transmission was not sustainable with an R0 value of 0.2 or below. Just as with the CFR debate, those values can differ due to different assumptions, definitions and methods.
Everything we know indicates that wearing masks would drastically reduce the risk of infection during an H5N1 pandemic. Of course this requires high quality masks and correctly using those masks.