I found this with a basic, quick Google search using the keyword phrase concealed handgun instructor for Kentucky:
Welcome to the Department of Criminal Justice Training
Then there's this one: Kentucky State Police: Concealed Deadly Weapons
There's also this link -http://www.lrc.state.ky.us/krs/237-00/110.PDF - but it seems to be the KSP's Rules/State Code with regards to Concealed Carry. A quick skim of the document doesn't specify the criteria for becoming an instructor.
I'd suggest you start at the first site and ask questions via their email link. If nothing else, give them a call on the telephone.
I know that doesn't directly answer your question, but I don't live in Kentucky - love Louisville and the rest of the state, tho! - and can only view The InfernalWebz for information.