As for white rock x BR, that's not automatic. White is not a color, it is a gene that simply prevents the bird from expressing whatever color or patterns it has. He could easily be a "BR" only you can't see it.
Also there's the problem of there being two main genes for white birds- Dominant White and Recessive White.
So.. if your WR is a black and barred and a recessive white.. then ALL of the babies out of him and the BR will be... BR. No sexlinking there..
If he's Dominant White then majority of the chicks will be either white or white-black or white-buff/red(that would be DW crossed with a Buff Orp). No sex linking there, unless he happens to be gold based and doesn't have the sex linked barring then you may be able to see some barring on the colored parts out of the BR hens.
Chicken color is basically divided between Gold and Silver. Gold is nearly everything that are mainly brown/red/buff.. so a Buff Orp is a gold base. Red is just gold with other genes that darken the gold to red(the Mahogany gene is one). Silver is nearly every chicken that are "black and white" such as Light Brahma(Buff brahma are exactly the same.. just on a wait for it.. gold base.). Silver also happens to be sex linked so, using this example, a Buff Brahma over a Light Brahma hen would give sex linked offspring. However, what isn't so well known is that very frequently both of the offspring will show "leakiness" or imperfect coloring such as the silver(light) cockerels very likely will show buff or red off coloring somewhere on their body.. not a good thing if breeding for show or trying to stay with a standard.
To use the barring for sex linking it is much simpler to use barred hens with colored roosters.. remember white is not a color. RIR or Buff or Black Leghorn etc.
The reason the major producers use "white hens" for sexlinked matings is because they bred those lines to be white AND also have the other sex linked genes(usually barring and silver). So it really is not "white is sex linked".. These hens mainly have Dominant white which just has the side effect of making the chicks easier to sex, as it affects mainly the black pigment.. the cockerels would be silver, barred with dominant white making them extremely light while the hens are gold, no barring so the only effect they get from DW are the white tails and wings with red bodies.
