It's quite astounding how little power is needed to produce visible light from a modern LED, there's a long running thread over on another forum about an LED from a party balloon using two LR41s in July 2015 and is still lit, albeit very faintly, as of 26th November 2016 on the same LR41 cells.
So, with that in mind, three possible sources of power spring to mind which might be worth investigating.
Light, Heat and RF
A single, non phosphor LED will work as a current source when illuminated by ambient light, it may be possible to use that to charge some energy storage device, maybe capacitors.
Hopefully your prospective partner will be warm, thermocouples might be useable, they produce very low voltages but at very low source impedance, might be possible to series connect a number to produce some workable voltage from body heat, ditto Peltier junctions.
It's possible to read non battery UHF RFID tags at ranges of 15 feet, ultra long range RFID is a thing, again you'd need to 'harvest' the energy and store it until you have enough to flash the LEDs. May also be possible to harvest enough energy from local RF to flash the LEDs occasionally and as most people these days have cellphones it could be workable to harvest some of that RF.