Sometimes a pullet will have the same colors as her father, but there are enough exceptions that I would not trust it as a general rule for sexing.
In this case, Buff Brahma father x Red Cochin mother would produce chicks of about that color in both sexes. (You said Red Cochin was one possible mother.)
And with the White Cochin mother, it would be hard to predict because there are several combinations of genes that can make a white chicken. One kind of white would give all white chicks in both genders, another kind of white would give sex-linked chicks (daughter matching father, son matching mother), and a third kind of white could give chicks of almost any possible color. If you like to look up genetics, I'm referring to Dominant White, Silver, and recessive white, in that order--with certain assumptions about what other genes might be prsent in each case. If you don't care about the details, I can shorten it to "white is complicated."