Absolutely pure water has a resistivity (inverse of conductivity) of 10 MOhm/cm^2. It’s a pretty poor conductor. However the resistivity quickly drops to 3 MOhm/cm^2 if you just expose the water to air because it will absorb CO2.
Conductivity is related to the number of charged ions present and their mobility. Vinegar contains acetic acid, which will dissociate into ions. So yes. Vinegar is conductive. It’s less conductive that a strong acid, however. It’s going to be more conductive at high pH, when it’s fully dissociated, then at low pH.