I assume that you're having issues with the York County Zoning and not the Rock Hill city zoning. I just filed my administrative appeal with York county today. In truth, there is no zoning ordinance that prohibits "pet" chickens in any of the zones. However, the zoning administrator has decided that "all chickens are agriculture" and agriculture is only permitted in the AGC and RUD zones. York County, however, lacks any laws or ordinances to support his interpretation. The State of SC, however, does have laws indicating that chickens can be possessed outside of "agricultural purposes."
I makes me a bit angry that I had to drop $300 to fight a violation of an ordinance that does not exist. It was even more frustrating that they refused to answer my emails and they refused to acknowledge my attempts to schedule a meeting with them to discuss the ordinances. Now all of my neighbors will get nice letters from the county telling them of my administrative appeal and a sign will be posted on my property. On Oct 8th, I'll find out if I just wasted $300 or if (hopefully) York County residents will be permitted to keep pet chickens.