He's singing with melodic embellishments.

Literal

He [topic-は] melodic-ornaments [object-を] working singing.

小節を利かせる (こぶしをきかせる) is a music term for adding melodic embellishments — the vocal ornaments (turns, runs, vibrato-like flourishes) characteristic of enka and min'yō (folk songs). 利かせて ('making effective/working') uses the causative of 利く. The sentence describes a specific Japanese vocal technique that has no direct English equivalent.