The first thing to do is repaint this:
You should get some Acetone on a cotton swap and go at that soleish area (remember to tape off the sole and midsole) take all of it off to get an even look for the whole shoe. Or you can just Acetone the part that's chipping the most and repaint the whole shoe at a later time. Then get some Angelu's (just plain old white) paint and repaint that area. Use small strokes going in one direction or paint it how you want to get the white paint to look as you wish. Also some people put on overcoats or finishes. Do that if you want but the first two steps are pretty much the minimum to get that looking like new.