Is there any particular rule for specific colours in adjective order?

From Mari-Lou and Ralph's point on dominance/prominence, I'd probably be more inclined to say black and white cat, e.g. for this fella‌​:

But white & black cat here:

If the mixture is equal, I'd probably use either order; though with something like black & white, I'd naturally go towards more common phrasing (e.g. we have black & white films/photographs, so that's feel more natural through use rather than a specific rule).

In a corpus of about 1.5 million words of poetry I found 214 instances of conjoined colours, where the colours were the 12 commonest colour terms in the U.S. frequency dictionary. Red and white occurred 12 times, and white and red 10 times. A 12 by 12 chart of all the possibilities exhibited a roughly symmetrical pattern of results with one exception: green and gold/en occurred 26 times (the highest total of all possible combinations), but only 4 instances of gold/en and green.

In common speech, black and red seem to be dominant: Christmas colors are red and green. The US flag is red, white, and blue. The primary colors are red, yellow, and blue. Zebras and penquins are black and white. We write things down in black and white. Opposites are black and white. Bruises are black and blue. The War of the Roses involved red and white roses. Ask people what color these things are, and the colors will almost always be biven in the same order. Silver seems to be dominant over gold: silver threads among the gold, London Bridge is fallinng down...build it up with silver and gold. These color orders are not a rule of grammar, but they definitely do constitute a shibboleth. (Saying it "wrong" brands you as an outsider.)