The day traces its roots to June 14, 1777, when the Continental Congress adopted the original 13 star, 13 stripe design for our national banner. Still, Flag Day hasn't become as important as other holidays. It isn't even formally recognized except in Pennsylvania on a state level.
Oh, it would just be shoved to the nearest Monday if it were made a full holiday. So maybe it's just as well that it stays on June 14 year in and year out. Your flag should fly everyday anyway.
Still, I miss watching that large old flag which would be unfurled down the face of the old downtown Hudson's store. I think it covered 11 of the 14 floors of building. It was pretty impressive. I saw it happen live twice as a teen, with my mother after dentist's appointments. That to me was Flag Day.