The effects of flu shots are generally thought to last 6 months. Sometimes children of greater risk will receive a second dose (so two in the course of a year) but there isn’t research to support a second dose in one season for adults. It’s not dangerous, but there doesn’t seem to be a benefit.
Anyway, sometimes the timing might take into consideration the prevalence of flu early in the season. If flu seems to be in your area I wouldn’t put it off too long.
I work in health care and our health system is just with the last week starting to give shots to employees.