And you'll find that a 1.5mm wide, 1mm thick, trace can carry 18Amps. That's obviously pretty large for a PCB trace, but not untypical for a microUSB-like connector.
But... this is all assuming we're using caps at ~5v. Seems like you might want to use significantly higher voltages and buck converters to power the phone.
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I don't think it works like that. Use a typical trace width calculator e.g.:
http://www.circuitcalculator.com/wordpress/2006/01/31/pcb-tr...
And you'll find that a 1.5mm wide, 1mm thick, trace can carry 18Amps. That's obviously pretty large for a PCB trace, but not untypical for a microUSB-like connector.
But... this is all assuming we're using caps at ~5v. Seems like you might want to use significantly higher voltages and buck converters to power the phone.