Start with your own community. Inquire with your county's emergency manager. Many county emergency management agencies (EMAs) maintain a volunteer SAR team. Many EMAs also have Community Emergency Response Teams (CERT), or county or neighborhood organizations that prepare for local emergencies. Some of these do SAR. County fire departments and sheriff's departments often have volunteer firefighters or "sheriff's posses" that do SAR as part of their community work. Even if none of these have teams dedicated to SAR, they may still be able to direct you to reputable and local private teams.
There are also some state-wide volunteer organizations that participate in SAR. The Civil Air Patrol (CAP) is the official auxiliary of the U.S. Air Force. CAP performs about 70 percent of the searches for missing U.S. aircraft. They search from airplanes and on the ground. CAP also participates in lost-person searches in the United States at the request of local, state, or federal officials. Members are civilian volunteers who wear US Air Force uniforms in the execution of their duties. CAP has squadrons throughout the Unites States.
Other sources for team references include the National Association for Search and Rescue (NASAR). You might also use Internet search engines such as Google to find teams. Be specific with your search terms such as Kentucky + wilderness + search and rescue to narrow down you Google search.