Pruners will work better and with less of a hazard than linseed oil and turpentine. If the mixture actually does kill off the vines you will still need to use the pruners to cut them down.

My suggestion would be not spraying something flammable on a structure. First step is identifying the vine so you know what you are dealing with and how to best approach it, a pic on the Name That Plant forum would work great.

Except to eliminate that the vine is Poison Ivy or Oak there is no real need to identify what it is. Just cut the vine off the building.

To make sure the vine doesn't just come back, after cutting it at the base you can put a drop of triclopyr* on the cut surface.

*Brush-B-Gone