Is that pure white or a light grey? Can't tell in the pictures.
What I usually do is grab a lighter colour of paint, and then whack that on the model where I want chips to be. After that, paint over the lighter colour with a suitable brown, leaving a really thin line of the lighter colour. This gives an amazing effect, here is my method.
Mephiston red basecoat all highlighted and pained.
Paint Troll slayer orange (Blazing orange) where the scratches are to be.
Layer Mournfang brown (Calthan brown) over the orange in several very thin layers.
Very very very light drybrush of a dark metalic on the edges (If there are any) to represent fresher scratches.
(Not the best quality image, sorry. But you can kind of see the effect)
But if your paint scheme is pure white, then replace the lighter colour with black/grey, should have a similar effect.