
Yes, according to a recent U.K. study which assessed the combination of Flu vaccines and COVID vaccines.
The well designed study found the combination to be safe. The study also found “the side effects of giving both vaccines together were generally well tolerated and acceptable”
There is a worry that Flu might cause severe problems this year compared to last year.
Everyone’s attention has been focused on COVID booster and many old people have not been thinking much about their yearly Flu shots.
It is important that elderly have the flu shots this year.
It is important to note that it is not unusual to combine vaccines. Lot of childhood vaccines are combined safely for many decades.

References
Guardian. Flu and Covid jabs safe to be given at same time, study finds
Safe for people to get flu and Covid jabs at same time, says study
Clinical trial finds reported side effects mainly mild to moderate.
ByNina Massey, PANick WoodMax Channon
00:15, 1 OCT 2021
CDC. Combination Vaccines. Fewer shots, but same protection

Disclaimer: Please note – This blog is NOT medical advice. This blog is NOT a expert medical opinion on various topics. This blog is purely for information only and do check the sources where cited. Please DO consult your own doctor to discuss concerns and options relevant to you. The views expressed in this blog are NOT, in way whatsoever, intended to be a substitute for professional advice. The blog is NOT previewed, commissioned or otherwise endorsed, in any way, by any organisation that the author is associated with. The views expressed in this blog likely represents some of the author’s personal views held at the time of drafting the blog and MAY CHANGE overtime, particularly when new evidence comes to light.