A flame will be as there is ionised particles in it but pure soot should not be condctive. But how conductive do you mean? Im talking a few nAs
A flame actually acts as a rectifier diode, some gas burners use the effect to detect if they go out. http://www.fieldpiece.com/tech-articles-flame-rectifier.htm Pure soot = carbon, a good conductor if a continuous film. One way of electroplating metal onto a plaster or rubber mould is to coat in soot first with a candle flame.
Many heavy smokers who smoke in front of their computers have noticed this when their computers suddenly stop working
There are some people here who know way too much for their own good haha. Man, every question and a professional answer.