Trouble getting AL8861 LED Driver to illuminate LEDs
I figured it out – it was two things:

Something in the board must have been soldered improperly, because I reflowed everything and tested all connections, plugged it back in and it was suddenly working as expected.

The LED isn't shining as bright as I would have expected because of the RS2 resistor value. The formula in the datasheet is Current = .1/R. Right now my RS2 is 6.34ohms, which is 15mA. To run this much higher, I will need a resistor value between .1 and .15 ohms (I didn't even know these existed).

Hope this helps anyone else out there with this chip!