Why does drinking cold beverages give you a flu ?Watch
A cold is caused by viruses. The flu specifically is caused by influenza virus. Drinking a cold drink has nothing to do with it, unless you drink a cold drink from a glass previously used by somebody with a cold or the flu and pick the virus up that way.
But that was on isolated mouse airway cells with a mouse adapted rhinovirus. And you still need to catch the virus itself as a pre-requisite.
To my current knowledge there's no real evidence for this one.