Yes, there are OE FIAT mudflaps.
I've seen two types - a small, rectangular shape promoted under 'FIAT Lineaccessori', and a larger, rounded shape with FIAT in white, which may have been a New Zealand-importer fitment.
The rear bumper has mounting 'ears' that are easy to screw into, though I think you're supposed to use clip-nuts. The front mudflaps are a slightly different story, as the front wing would need to be drilled, presenting a corrosion risk. I don't think I'd bother personally! But that's just my opinion.
If you're concerned about stone chips along the sill, why not fit the sill covers and wheelarch covers from a Turbo? Or, just a few minutes with a spraycan of black paint should smarten it up?
-Alex