Hi Willi,
Figure 4 shows the IC's supply current with only a 15uA load current. You won't see an LED that has only 15uA through it. :cry:
A constant current source is an automatically variable resistor in series with the load. It is used to keep the current constant through an LED as a load that is continuously turned on, when its power supply voltage is changing.
If you are using PWM, it can keep the LED's brightness constant if the supply voltage changes, then you won't need a constant current source that wastes power.
I don't think your shaker makes enough power for an LED flashlight.
Maybe now you are talking about using a low PWM duty-cycle so the average current is low. Low average current in an LED results in dim brightness.
Maybe you are talking about blinking the LED so it uses less power. A blinking LED makes a lousy flashlight.
I made some, they are an ultra-bright LED that blinks with five 100mA pulses about 20ms each in duration, at about 10Hz, with a 1 second pause in beween. Because they blink very brightly, they attract a lot of attention. Because they are off most of the time, their battery lasts a very long time. I can shine one on the ground at night to see where to walk, but the blinking and pauses aren't good for a flashlight.
My ultra-bright chaser projects make pretty good flashlights, when their PWM is turned up to max duty-cycle and their speed is also max so they are spinning like mad. But then they draw lots of current, about the same current as a single LED, and require probably much more power than your shaker can supply.