I haven't had the shingles vaccine yet so I can't speak to that, but for at least the past 3 years I've gotten COVID and flu vaccines at the same time in the same arm (this year included).  No problems other than typical arm soreness for a day or two I really had no other reaction.  DH has gotten COVID and flu both spaced out and together and he always reacts to the COVID one either way.  Nothing earth shattering, but definitely chills, fever, and sore joints etc. for a couple of days.