It’s absolutely fine to have a flu and Covid vaccine together, with any vaccine you can feel a little bit out of sorts around 12 to 24 hours later like you ve got a cold coming on and you may get a localised reaction like a bit of an achy arm all of which are normal side effects, we re all different and we all respond differently to medications and vaccines, some may have no side effects and others may feel some mild cold like symptoms.
Just fyi I am a vaccinating nurse even at the ripe old age of 67, going for my Covid jab on Fri