5V Switching Regulator Problems
That flashing makes me think there's a bad spike happening at switch
  on time.


I think you are on right track. The problem is likely in start-up transients.

From the PCB layout: it is customary to place a de-coupling capacitor in close proximity to every Vin entry point to any sub-block, be it a IC or an external module. There is no cap at the entry to NRF8001, the module which has died.

I also tried to imagine the shape of bottom ground plane (I assume it is there). It looks like it is badly traversed by many signal traces, so the actual ground integrity looks very questionable. 

So I am afraid this board has strong transients that killed your NRF module. Try to put a 10-uF ceramic 0805 capacitor between Vin and GND pins on the NRF connector, and maybe put some 5-V voltage suppressor.