From a purely practical point of view, the board has to be cleaned after every use and I have doubts about how easy or difficult it would be to remove sticky linseed oil.
In my view, vaseline or ordinary vegetable cooking oil does the job of keeping the debris on the board until you get round to counting mites and it can be wiped clean very easily.
CVB
Linseed oil is sticky only because it hasn't dried properly, or has been put on in damp conditions and or too thickly.
Correx board works well. Thats the plastic signage often used by estate agents and political parties. Its free of course if you can get some. Just be sure to fill any cut/open edges with something like clear silicon. Its constructed like cardboard, and the corrugations are great places for earwigs and the like.