Height is a matter of personal taste. Typically lamp chimney rises 2″-4″ above top of lamp shade.
Bottom diameter is measured outside edge to outside edge. Most burners have a narrow seat for chimney to rest on.
If having trouble getting an accurate diameter. Test by cutting a ring to needed diameter. Slip down over burner to check fit.
Fit: The chimney should put slight pressure on the tines of the chimney holder or burner which in turn holds the oil lamp chimney in a stable position. This ensures a proper updraft enabling the burner to function correctly. Make sure chimney fits securely if using on an oil lamp.