Truthfully, I'd just say that the white hairs in his mane are just part of who he is as a chestnut and they aren't being caused by any particular gene (not one that's been identified anyway).
My chestnut draft cross (who isn't flaxen) has started developing some white ticking in his coat in the last year (he turns 4 in July) and he's started to get the white hairs in his mane as well...that he didn't have a year ago. I actually pulled one of his hairs out today that was red for about 3 inches and then transitioned to sort of a clear color and then to white. It was like a person who needs a dye job because their roots are showing LOL.
Hey- that's what most of my hair looks like too, lol. I need a dye job! very interesting how they can be born with such fabulous hair! I guess us humans can be too.. just not me.. Im goin grey!