I agree with what has already been suggested, start with some kind of mixture for an off white. With an airbrush, prime the whole figure with this. Mix a second shade that is halfway between this and white, and spray from a top direction down to about 90 degrees - this will represent your mid tones while the first layer will be shadows. Then from directly on top, spray white as this represents highlights.
Now you can go in with a fine brush to add more contrast to shadows. Personally I avoid washes in terms of slathering the whole figure and hoping gravity does it thing. Precise pin washes are fine though for areas such as waist belts or buttons for example.
As far as dirt goes, no they definitely don't roll around on the ground like infantry, but I think you'd still find some dirt on them. If one stepped in a puddle some mud would splash upwards. Walking around their transport vehicle could also transfer some dirt. I'm also sure their flak gun wasn't in pristine museum condition, so to some lesser degree dirt/grease from this equipment. The crew likely transfers mud from their boots to the gun platform, and it is possible someone knelt on one knee in that mess.
As always, the old adage less is more is a good rule to follow.
I posted this pic as it shows a good pattern of dirt on the lowers, ideal for what you are doing.
regards,
Jack