When the CDC released its latest round of recommendations regarding seasonal flu vaccines, the agency made one notable update: Flu vaccines and COVID-19 vaccines can now be given simultaneously.
The guidance is a marked change from previous agency recommendations, which said that other vaccinations should not be administered within a 2-week window before or after the COVID-19 vaccine.
Source: WebMD
https://www.webmd.com/vaccines/covid-19-vaccine/news/20210916/cdc-safe-to-get-flu-covid-vaccines