Well, yes and no. Thinning any finish to put in the checkering is a good idea since the checkering holds the finish well anyhow. My experience though with linseed oil is not the greatest. It does not seem to get as hard as many other finishes. I would consider tung oil or Tru-Oil over linseed oil. It is also a minor change, but I like turpentine over mineral spirts as well, but both will work.