Besides the already mentioned max. amperage of 1.4 A (Maximum amps for chassis wiring) / 0.23 A (Maximum amps for power transmission) (see here for further insight) there is another issue to consider - voltage drop along the wire:
Assuming 1 A drawn by the Pi and additional peripherals (note this could be different depending on the peripherals and load case of the Pi). Consider the power supply provides 5.25 V (acceptable max. voltage, make sure as the charger/power supply might not hit that limit) and at the far end a voltage of 4.75 V is required (acceptable min. voltage = input voltage of the Pi). So a total voltage drop of 0.5 V is allowed. So with
U / I = R = 0.5 V / 1 A = 0.5 Ohm
the max. acceptable resistance of the wiring is 0.5 Ohm. AWG28 has a resistance of 0.21 Ohm/m. So, assuming 1 m distance between load (the Pi) and the power supply - equals 2 m of wiring (back and forth) - the total resistance is already bordering acceptable limits.
So it really depends on the length of the ribbon cable wiring. If it is possible to use multiple strands for powering (both VCC and GND!) a wider margin of safety will be achieved.
Update to reflect question's edit:
With a length of 10 cm the total resistance will be 0.04 Ohm and at 1 A a voltage drop of 0.04 V which would seem perfectly acceptable.