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. 

Watch Joe ishoot the cuffs/i before he goes up to that chick...that shit drops panties.