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

Solution 1:

I mean is it preferable to say:

red and white flowers Or:

white and red flowers

Or is there really no grammatical rule to obey?

No, there is no rule, you can use any order you like:

"There were white, red, purple and pale-blue flowers on the table" is correct with any permutations of the colours

Solution 2:

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.

Solution 3:

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).