I want to say
She has long, straight, black hair.
How do I say it correctly in French?
Elle a de cheveux longs, raides et noires.
or is this order wrong?
This form is current in the written language. In the spoken language you can still use it (it will not sound as an excess of formalism); you can however opt for other possibilities, for instance if you want to insist slightly on one of the charateristics it's possible to use an other word order and, if you wish, a particular intonation on the first adjective; it is however important to remember that you can use "de" only in (1) above; when the adjectives are after the noun you must use "des".
Elle a des cheveux raides, longs et noirs.
(longs, raides et noirs), (noirs, raides et longs),…
Strangely enough, you can't say the following except perhaps in poetry;
Elle a de raides cheveux longs et noirs. Elle a de noirs cheveux longs et raides.
In English, the adjectives are very easy to use, you just put them before any noun, and they will define their meaning on their own. However, in French, the usage and the placement of the adjectives vary. And, their usage also depends on whether the noun you are using is masculine, singular, plural, or feminine.
Describing hair length in French:
• les cheveux longs- long hair
• les cheveux courts- short hair
• les cheveux mi-longs- mid-length hair
For example Elle a les cheveux longs( she has long hair)
Hair color in French:
• les cheveux blonds- blonde hair
• les cheveux bruns- brown hair
• les cheveux gris- grey hair
• les cheveux noirs- black hair
• les cheveux roux- red hair
However, in French, there is not really order of adjectives; there aren’t any rules like in English. But, you can put conjunctions like " mais, ou, et, or, ni." Which means “Elle a des cheveux raides, longs et noirs” is correct.