What is the most natural way to describe the color of an object as a combination of blue and white? For example we prefer "black and white" to "white and black". Does it matter which color is predominant?
It's interesting to compare the usage of both orders in the Google Ngram Viewer. In almost all cases, white comes last:
Black (about five times as often):
Blue (about two times as often):
The only exception I could find was yellow, where it's about equal:
Roughly, the order seems to be
red > black > blue, green > yellow, white
In general, the combination with and seems to be preferred over the hyphen:
Particularly for those of us who learned colors from Crayola crayons, the hyphenated form usually represents a blend of the colors — yellow-orange is a single color, of a hue somewhere in between yellow and orange.
There are several common irreversible binomials, notably black and white and black and blue (when referring to bruising). In some other cases, a particular order has become idiomatic. The colors of Princeton University are always orange and black, never black and orange. The American flag is the red, white, and blue and Team Australia the green and gold.
It is difficult to reduce the patten to any kind of rule for general use, however. In pairs, I think the more distinctive color naturally comes first, so the Greek flag would commonly be described as blue and white. On the other hand, the colors of my high school were always given as black and gold, because black was the primary color, and gold only used as an accent.
Ultimately, at least if providing a simple description, I do not think you need to be overly concerned about order. I do not think anyone would object to listing the colors of the Japanese flag as either white and red or red and white.
You won't notice the difference in spoken language, but another option is to separate colours with a slash, for example "green/yellow" or "black/white" to denote those combination of colours. This is very common when describing objects in product listings or technical specifications, less so in more literary uses.