Does a med spa have to register or hold a license in Kentucky?

Short answer
The cited rules do not settle this — there is no med spa–specific registration; a premises where esthetics is done for the public or for consideration is a "salon" (initial fee $100), but Chapter 317A does not reach physicians' incidental esthetic work.

Kentucky licenses the PREMISES through the cosmetology board: a “beauty salon” means any establishment in which the practice of cosmetology is conducted for the general public or for consideration, and practicing in an unlicensed salon — or in a salon knowing it is not in compliance with the chapter or the board's regulations — is a ground on which the board may refuse, suspend or revoke a license or permit, impose probationary conditions, levy an administrative fine, or reprimand. A “cosmetologist” is a person who engages in the practice of cosmetology for the public generally or for consideration, regardless of the name under which the practice is conducted, and an “esthetician” is a person licensed by the board to engage in esthetic practices. These claims survey the cosmetology chapter and do not report on registration requirements elsewhere in Kentucky law. On compounded drugs the Board of Pharmacy’s compounding regulation is direct: preparations compounded for human use shall NOT be essential copies of a commercially available drug product unless authorized by 21 U.S.C. 353(a), and an essential copy is one with the same active ingredient in the same, similar or easily substitutable strength by the same route — unless a prescriber determines a change for an identified patient that produces a significant difference for that patient.