In 1989, Béla Fleck was in a bit of a predicament: He found himself scrambling to find a band to back him for a PBs Lonesome Pine television special. Given the short time Fleck had to assemble the Flecktones, the outcome is amazing. Since their formation, Béla and the Flecktones have recorded five records, one of which made the No. 1 spot in the Billboard jazz chart, played a huge number of live shows and festivals and won five Grammy nominations.

“I think it was supposed to happen,...