If he carried the dilute gene it would have shown up, he would have been palomino.

Both parents were Ee for the red gene, (that is the only way to get a chestnut from black parents - bay is black modified by the agouti gene) he carries ee so no black from his side. If he were bred to a horse that is black or bay he would have a chance of throwing chestnut, bay or black.

If the mare were homozygous for black, foals would be black (or bay) only (+ any modifiers from the mare's side).

If he carries the Frame Overo gene, it would be important to be sure the mare does not carry it as well. Two frame genes passed on = Lethal white.

Finally he may or may not carry the agouti gene, only testing would tell as it does not show on a red horse.

You can learn more here: Horse Testing - Equine Genetic Testing and by Googling equine color genetics

What are the breedings? AI or Live cover? If the latter, where is he located? I may know someone.