Yes. You can get a COVID vaccine and other vaccines, including the flu shot, at the same visit. You no longer need to wait 14 days between vaccinations.

Experience with other vaccines has shown that the way our bodies develop protection after getting vaccinated, known as an immune response, and possible side effects of vaccines are generally the same when given alone or with other vaccines.

SOURCES:
https://www.aarp.org/health/conditions-treatments/info-2021/when-to-get-vaccines.html (AARP)
https://www.cdc.gov/coronavirus/2019-ncov/vaccines/faq.html (CDC)

Updated 12/16/2021