IMHO much better question is that which nations have flags that DON’t have blue, red or white in them? As those are coloures that are in most of the flags.
Jamaica (black yellow green) is the only national flag I can find that contains no red or white or blue.
Bahamas is borderline, I’d call it greeny-blue + yellow and black.
Sri Lanka (green orange yellow maroon) is another borderline, the “maroon” pretty reddish.