Yes, I went to my collection to look. The Skinner 3-Ring routine is on A-1's Michael Skinner's Classic Teach-in Series, Volume 1: Linking Rings.
Also, I had almost forgotten this in my collection, but Stevens Magic has a great ring video with Richard Ross, Max Hapner, Jay Marshall, and Samual Patrick Smith. The routines of both Ross and Hapner are 3-Ring, plus the 5-Ring of Marshall and the 8-Ring of Smith have plenty of ideas to incorporate into the smaller ring set. The video is Linking Rings: The Greater Magic Video Library Teach-in Sessions.
With those listed in posts above, plus Skinner's, Ross's, Hapner's, and Ganson's from Art of Close-up Magic, you should have plenty of good ideas and approaches from which to draw.