Controlling 4x4 LED matrix with Huzzah Feather and 20-pin shift register
Without a schematic, I'm not sure how you've connected your LEDs, but I doubt it's what you want. 

At any rate, you'll need to specify 3 of the 9 GPIO pins on the Feather as your 3 control lines, then write a program to toggle them appropriately to shift data out to your S/R, then toggle the latch line.