When the leds are flashing It means the driver is working. The unipolar stepper (yours) is a motor runned by 4 coils, the leds show you which coils are powered up.
Lucy:
(this is without even trying to run the arduino code) it is just from plugging it in(my actual drawing was a bit small but it came out ok in photo)
When you power Arduino it runs the last code you uploaded (it has memory).
Why dont you try increasing the speed rpm in the code? Maybe your stepper is working but it is doing real slow steps.