Italians are famous for the amount of hand gestures they use when communicating, and it is possible to convey everything from 'do you have a smoke?' through to 'you're lying!' with a simple hand gesture.
'Flipping someone off' usually refers to raising your middle finger and showing someone the back of your hand. This has become a universally offensive gesture so, in short, the answer to your question would be that Italians use much the same gesture as anyone else would to 'flip someone off'.
However, there are a plenty of other commonly used offensive gestures that Italians have in their arsenal, a few examples of which are:
I'll kick your ass!
Making a gesture with the index finger and thumb of both hands as if showing the size of something is one excellent example of an offensive Italian hand gesture. This gesture is often accompanied by the phrase Ti faccio un culo cosi which means something along the lines of 'I'll make your ass like this' and is the Italian equivalent of 'I'll kick your ass!'
What do I care?
By brushing your hand against the bottom of your chin, you can show someone what little regard you have for something they have said or done. This gesture is often accompanied by che mi frega or 'what the hell do I care?'
The horns
Making a horn like shape with your hand and sneakily placing it behind the head of your unsuspecting victim is one of those childish pranks that delay the proceedings when class photos are being taken in Italian schools, but the origin of this gesture is actually quite inappropriate and is used to signify cuckold or the fact that a man has an adulterous wife. In Italy, this gesture is commonly directed at referees during football matches when a decision they make proves unpopular.
