No. Vinegar is not flammable. See fire and explosion data for vinegar below:
Conditions of Flammability: not flammable
UFL: not available
Flash Point and Test Method: not available
LFL: not available
Sensitivity to Static Discharge or Mechanical Impact: not available
Auto-Ignition Temperature: not available
Hazardous Combustion Products: not available
Means of Extinction: not available
An SDS (Safety Data Sheet) for vinegar provides a comprehensive information its properties, the physical, health, and environmental health hazards; protective measures; and safety precautions for handling, storing, and transporting the substance or mixture.
Interlinebrands.com - Safety Data Sheet: Vinegar, all varieties
esciencelabs.com - Flexo Material Safety Data Sheet: White Vinegar
Columbuschemical.com - Safety Data Sheet: Vinegar
The bulk of the chemical and physical properties of vinegar come from its two major components, which are acetic acid and water.
It’s the product of two biochemical processes. These processes are alcoholic fermentation and acid fermentation. Alcoholic fermentation converts natural sugar to alcohol.
Acid fermentation converts alcohol to acid via microorganisms, which are present in the air, we breathe, called acetobacter.
The acid part of vinegar is what gives it its sour taste and its antiseptic (germ killing) properties as well as its cleaning properties. See more at Enzyme-Facts.com.