Hi there. You don't need books here
That resistor had 1.5Ohm value before it had burnt (7kOhm now, right?) And 1.5 it's almost "zero" resistance. So you can
short R1' terminals with a thin wire, and then plug in the flash into USB port.
p.s. For a quick test such solution will do, but for a long term operation you have to solder in there a real 1-2Ohm SMD(surface mount device) resistor.