As for how you got the "effect": My guess is that you were too far away for the weak flash on the phone to do anything other than produce the red-eye, which means the phone still had to increase the exposure (probably via high ISO) to the level required by the available light anyway, blowing out the red in the red-eye in the process.
It's not difficult to fix manually with a paint program like GIMP, just view at 2:1 (200%), and use the smallest brush available.
ADDENDUM: The reason the flash was low-power in the first place may have been because the camera was metering (at least partially) on the bright white paper the girl is holding.