The Cross has practically* same ground clearance as the current 4x4, and both have less than the previous model. Neither has as much as the Mk1 had.
The Cross has plenty of plastic protection on the side panels to deflect stones etc already, so not sure that flaps would be needed. And anyway, they're supposed to be muddy! That said, my 4x4, in the least appropriate colour for anything going off road (white) actually had a wash over the weekend, after a few miles along byways of North Herts. Prior to that it was mostly brown, which I think rather suited its chunky looks, but the windows and lights had become less effective!
*the ever-so-slightly taller tyres on the Cross add a few mm, but no mechanical changes from 'normal' 4x4.