Are switch blades illegal in Kentucky?

No, it is not illegal to own a switch blade knife in the state of Kentucky. Kentucky has no laws prohibiting or limiting the ownership of knives but when it comes to carrying them on your person, it has to be an "ordinary pocket or hunting knife". And for the rest of the carrying laws, it is dependant on your local jurisdiction.

Short answer; it is legal to own but not necisarily carry dependant on the laws of the local jurisdiction.