I am having an attempt to hatch eggs. First try doing this, it’s soooooooooooooo hard to wait!!!!!!!!!!!! It is a Cornish rock hen, and a barred rock rooster.
Their are two different ways typically used to make a solid white chicken like the Cornish Rock, Dominant White based on Black or Recessive White with who knows what hiding under that white. There are different lines of Cornish Rock, I'm not sure they all use the same way to get to the solid white look.
I'd think that most Cornish Rock will be Dominant White over a solid Black base. In that case you should get solid white chicks in the first generation. If you cross the offspring then solid black and black barred chicks will show up, but most will still be solid white chicks. So I'd expect your first hatch to be solid white.
If that Cornish Rock happens to be based on Recessive White, anything could be hiding underneath. But your Barred Rock rooster will give both Barring and Black to all his offspring. Barring is dominant so all the offspring will carry barring. Any non-white feathers should show this barring. Some genetics can modify Black to make it look different but Black is pretty dominant. While different things are possible I'd expect the chicks to look like their daddy, black barred.
So my expectation is that you will probably get all white chicks but exceptions are always possible.