Watched it last night, such an amazing costume!
You produce that speckle finish using a spray gun with adjustment for air, paint and fan (width of spray pattern).
Process: add the thinned paint to the gun, close the needle so the amount of paint going through is reduced, open the fan slightly and then turn the air down to almost nothing and then gradually increase until you start to achieve the speckle effect.
It's very much trial and error with you testing on scrap pieces of material.
Paint is generally a bit thicker than for normal spraying.
This is a technique we use on our architectural and display models.
Hope this helps.