Any flu vaccine has a well known, very rare, complication of GBS ("french polio") every year. The swine flu vaccine had a higher incidence. Read the fine print when you get the vaccine, it is mentioned there. During slow news times, the news people usually dig someone out who had GBS during flu vaccine time.
As the CDC says, GBS can also result as a consequence (sequelae) of flu. I'm guessing, but GBS will likely be shown to be a sequelae of COVID disease, among many other conditions.
We'll probably see such things with these vaccines. I'm still going to get the vaccine earliest I can because COVID causes all kinds of long term issues.
Source, from the CDC:
https://www.cdc.gov/vaccinesafety/concerns/guillain-barre-syndrome.html