I have fixed a similar problem on an Alfa Giulietta. It looks like the Blue&Me unit is ‘sensitive to failure’ throughout all FCA cars.
If you have one or more symptoms like a drained battery, a flashing odometer and the Blue&Me unit is not working properly, chances are high it’s because of a faulty Blue&Me unit.
To stop the drain you should unplug the unit, or remove the fuse if the B&M unit is the only thing using that fuse. Before unpugging the unit I would recommend to disconnect the battery, this will avoid an unerasable fault code that could trigger flashing of the odometer.
More information can be found in the video on youtube:
