Several small specialist manufacturers now market linseed oil as the binder in their paints, on the basis that linseed oil is greener than modern alkyd formulations (linseed is extracted from crushed flax seeds)
Traditional linseed oil paints were characterised by slow drying (significantly improved by addition of driers), rapid yellowing of the film and a tendency to support mould growth. The yellow colour of the oil could be a drawback in white or pastel shades. This led to the development of synthetic alkyd resins from the late 1920's which provided improvements in drying, film yellowing, mould resistance and general appearance e.g. gloss, colour purity. It would be difficult to provide an assurance that linseed oil paint can be over coated with Weathershield Exterior Gloss System but, providing the coating contains no wax additives and is obviously fully dry and with no residual tack, it may be acceptable after a light rub down and a successful test application.
We would suggest obtaining a data sheet in the first instance to try and establish specific content references e.g. wax, claims etc. If you have the product name this can probably be sourced from the internet. The presence of any natural waxes in the paint will make stripping essential.
However, it would be difficult for us to endorse the full 8 year performance from Weathershield Exterior Gloss System unless stripping back to bare wood is undertaken.