the aggregate of all his previous flight times:
(a) during the period of 28 consecutive days expiring at the end of the day
I think you are attempting to read something in to that statement that is not there.
It says 28 consecutive days, not 28 flying days, 28 duty days, 28 working days, 28 days excluding bank and public holidays.
Take the expression "the period of 28 consecutive days expiring at the end of the day on which the flight begins" first, work out what it means, and then work back from that.
Consecutive:- Following one after another without interruption
Mike