What are your goals? What do you want the chicks to be or do?
If you want to get into the genetics of shell color, here is a pretty good article about that. I suggest having a few Tylenol handy if you try to study it. It sure makes my head spin.
http://www.maranschickenclubusa.com/files/eggreview.pdf
A very simplistic way to look at your situation is that the base color of your eggs with those breeds will be white. A brown egg is simply brown pigment in addition to that white. I’ll assume your red hens are laying brown eggs. The leghorn rooster will contribute genetics that produce white eggs. So when you mix those you will probably get a pullet that lays a brown egg, but it is very likely it won’t be as dark brown as the red hens are laying. If you get a Rhode Island Red rooster, he will contribute brown shell genetics so you will get brown eggs out of that cross. The exact shade of brown can vary even between pullets with the same parents. That’s probably the answer you are looking for.
By the way, there are several different genes that can contribute to the brown. It’s not just one brown gene and those can be really mixed up. That’s why you can get so many different shades of brown.
But with the leghorn, it’s a little more complicated than that. The leghorn might or might not have genetics that block out some of the brown. You just don’t know by looking at the egg what genetics are there. I just learned that a couple of weeks ago.
So if you cross the leghorn rooster over your brown egg laying red hens, you will probably get:
Base white from both breeds + brown from the red hens = brown eggs.
But there is a small chance you could get:
Base white + brown + a dominant brown restriction = brown or white eggs. It just depends on whether that brown restriction is dominant, what browns it restricts, and what browns are present. Odds are still pretty good you’ll get a “brown” egg, but it may be even lighter than you would expect.
Do you start to see why I suggested the Tylenol? This stuff gets complicated fast.