General synonyms:
* Communication skills
* Composition skills
* Literary skills
* Expression skills
* Verbal skills
* Penmanship (for handwriting)
* Wordcraft
* Prose skills
More specific synonyms:
* Storytelling ability
* Persuasive writing
* Technical writing
* Editing skills
* Copywriting
* Journalism
Informal synonyms:
* Word wizardry
* Fluent pen
* Articulation
* Clever with words
The best synonym for "writing skills" will depend on the specific context and the type of writing you are referring to.