The sickness that accompanies heavy consumption of alcohol, usually, but not necessarily vodka, and that as a result causes a person to call out of work for a sick day.
The word has its origins with office workers looking to avoid being fired for not showing up at the office. Often, office workers have a limited number of vacation days and after a heavy night of binge drinking must take a sick day or risk losing their job. If required to specify a reason for their absence, the common response was to say they had the flu.
Julia drank heavily most nights and in the morning she was so hungover she had to call out sick because the vodka flu was keeping her bedridden.