She is stunning!
IMO she is a chestnut with flaxen. She has no dark points so any black based color, (Bay, Buckskin, Black etc) is out (without a DNA test saying she is E/e or E/E).
I assume that by putting her mom's color at "chestnut" you think she may not be chestnut. The only way to be 100% sure is a test, as mentioned, but good quality pics of mom and dad could help.
We all know that a registry will pretty much register a horse however you want to describe it so there is a slight possibility that she could be a palomino, however it seems highly unlikely.
She is far too red to be a palomino, despite the fact that it is not genetically possible anyway. I know there are dark palominos, but they are all varying shades of gold. Even the reddish ones have gold tones to them. This mare does not. However, if it really does matter that much, just pay to test her. If in the rare chance she does end up being palomino, someone somewhere else is wrong.