Lots of people are taking both at once. You can also space them out a week or two if you prefer. Which one to get first is up to you.
This year’s flu vaccine has two updates from last year, two newer strains replacing former ones.
If you don’t want to get them at once, and are decided which one to get first, you can guess how protected you still might be from your covid vaccines. Did you get moderna? When did you get it? How old are you? Do you believe yourself to be immunocompromised or high risk?
Protecting yourself with KN95 or N95 masks helps protect you from both obviously if you prefer no to get vaccinated for one for some reason.
Here is the current flu map, it’s starting to creep up a little in some states. https://www.cdc.gov/flu/weekly/usmap.htm Flu usually comes here by plane and ship, and with the mask precautions that should be hampered a little, but I expect domestic holiday travel to be huge, and there often is a big flu bump after the holidays and late January when kids return to school after all of that family visiting.
282 people already hospitalized from flu this season if I read it right. Many more from covid obviously.