Sounds like the original Blue & Me unit that came with the car has been unplugged from the Canbus. Unplugging it from the Canbus makes the Odometer flash.
In all likelihood when the Parrot was fitted, the Blue & Me was unplugged by the fitter. Try plugging it back in. It's behind the aluminium centre fascia, just above the air con unit. Just hope they didn't chuck it in the bin. As it's easier to unplug than unscrew and remove, you may be in luck.
When I had a stereo fitted to my Brera, I got the fitter to leave the Blue & Me connected to the Canbus but disconnected its inputs and outputs. Hey presto - aftermarket stereo working perfectly and no flashing odometer.
Brat Pack no.8