You can get preservative-free (thimerosol-free) flu shots if you have fears about
that. Thimerosol is only in the multi-dose vials.
/www.cdc.gov/vaccinesafety/concerns/thimerosal/index.htmlI am on 30mg prednisone and have been on 20mg-40mg since March 2017 and will be getting my flu shot on Friday.
The only concern with the being on prednisone (or any immunosuppressant) and getting the flu shot (or any vaccine) is that you may not have as good of a response to the vaccine due to being immunocompromised. However, that reduced effectiveness is very minor. It is still WAY better than not getting vaccinated at all.