Whatever colour either of the parents are the foal could be, and it could just be any random colour, but the most common is the colour of either of the parents.
A buckskin horse carries three important colour genes: the black gene, the agouti gene (which restricts the colour to the points, creating bay) and one dilution gene (changing bay to buckskin).
If...
This sounds unlikely to me.
A chestnut horse does not have any dilution genes in its coat. A chestnut with one dilution gene is a palomino, and with two dilution genes is a cremello.
A bay horse...