Jean:
By "thickened" linseed, I assume you are talking about Stand Oil? I think a better medium might incorporate a small amount of a resin (Canada Balsam/Venice Turp) or a varnish (Damar) - for better adhesion. I make a nice medium that incorporates Stand Oil, Canada Balsam, and oil of spike lavender (or turps) that works really nicely.
I don't use OMS or MS in paint, but do use it to clean brushes. I just don't think it mixes with oil paints as well as turpentine or spike.
I know that was not the answer you are looking for, but options are always good to consider...