I just visited Kiawah 2 weeks ago. I have been there perhaps 6 times in the last 5 years.
Charleston Co SO and Charleston Co EMS have jurisdiction on Kiawah and are dispatched via talkgroups on the Charleston County P-25 trunked radio system, SysID 1D9.
St. John FD covers Kiawah for fire protection and they are dispatched via analog talkgroups on the older Charleston Co. trunked radio system, 2822. Kiawah Island also has a talkgroups on this system, and it is active from time to time. Not sure if it's used for security or other coordination of services.
Kiawah Inn and Resort has 2 active UHF frequencies.
All of those talkgroups and frequencies are listed in the RR database on their respective pages.
I am always disappointed by radio coverage on Kiawah. Reliable reception where I stay is challenging at best. I can sometimes find a sweetspot and get okay reception of 2822. The PRO-96, the radio I'm currently using, is pretty poor at decoding P-25 simulcast trunked systems (CPSQK modulation) so I didn't get much on CCSO or CCEMS talkgroups at all. Perhaps it's my particular location - there is a large commercial communication tower within 1/4-mile with just about every provider co-located, that could be causing quite a bit of desense on my radio.
YMMV, and I hope you have better luck than I do.