In case of an EMP, those LED flashlights might not work. Keep a couple incandescents in your storage. They might not be as efficient or long lasting, but not much can go wrong with a circuit of a battery, switch, a couple wires and a bulb.
Highly unlikely that an EMP will affect LED flashlights or headlamps. There is not enough wire attached to the LED for the EMP to have effect. If you wish to be sure, put the led in a metal box like an ammo can.