Evidence?
The swine flu vaccine that killed people was from 1976 (increased rate of GBS which kills some people and was the underlying cause of death here) and was pulled. There's been a substantial improvement since then in testing modality, again in the 90's and again in the 2000's.
Following h1n1 showing up in 2009 there was this study which of course made waves as it should:
Risk of Guillain-Barré Syndrome Following H1N1 Influenza Vaccination in Quebec
This was highly concerning because GBS is the primary autoimmune worry from vaccines. It's rare, but it should be even more rare than that...even though you are more likely to get GBS from the disease(!!!) the vaccine needs to be safer than that by standards set today.
Turns out in a larger dataset
https://www.nejm.org/doi/full/10.1056/nejmoa1008553
It was safer. Does not increase GBS. Since then, continued studies show the same.
Just an FYI, H1N1 vaccine has been in several flu vaccines (I'd have to review the years) since then including this year. Again without increase in death or GBS.