Hi @CarlR - Thanks for reaching out! Kentucky has so much great land to roam around. It's great to hear you're planning a trip.
From my time in the Red River Gorge I know that people love section hiking the Sheltowee Trace Trail. In total, the Sheltowee Trail is 323 miles, but sections 12 and 13 (on the map on the site linked above) take you along the Red River and are right around the distance you're looking for.
Another good option is the Ridge Trail in Cumberland Gap State Park. It is a neat 21-mile trail that hugs the top of the Cumberland Ridge. While it is a well maintained trail, there were not blazes to follow the last time I was in that area. You might want to contact the park to know what to expect in regards to navigation. If you do head that way, be sure to stop by the impressive sand cave! It shouldn't be missed.
Let us know if you have any more questions and we'd be happy to help. Happy hiking!