The term refers to the habit that some men had of flicking their wrists in order to show the cuffs of their sleeves, and the cufflinks. The phrase goes back to the days when celluloid collars and cuffs were the salesman's answer to the laundry problem when on the
road. With the high-buttoned jackets of the period, the collar and cuffs were all that showed, and since celluloid could be wiped
clean with a damp cloth, a
shirt could be made to last a week.
Dandies would like to ostentationsly show their cuffs in a sudden and showy
way.
It is also called "to shoot
one's linen" in an unnecessary display of shirt cuff.