Yes. The CDC recommends that everyone 6 months and older get a flu vaccine every season, which occurs in the U.S. in the fall and winter. The best time to get your flu shot is in September or October before the flu is spreading in your community.
Based on CDC guidance, the COVID-19 vaccines can be given the same day as other vaccines, including the flu vaccine. Some people choose to get each shot in a different limb to minimize possible discomfort. Ask your health provider if you have any questions about getting either or both vaccines.