Genetically we don't know what makes one chestnut lighter or darker than another, so we can't differentiate for certain. Feed can make a huge difference, too, so essentially, how can we know it's genetic and not environmental?
However that being said it is thought that both flaxen and sooty are genetic, pangare most certainly is [why else would it be seen more in some breeds than others?], and I have known several mares that throw chestnut foals of identical shade to themselves. In theory, it COULD be passed on, we just don't know the genetics.