Involved in the dimethyl sulfide degradation pathway. Catalyzes the NADH-dependent reduction of FMN. FMNH2 + NAD(+) = FMN + 2 H(+) + NADH kcat is 14 sec(-1) for FMNH(2) as substrate. kcat is 10 sec(-1) for NADH as substrate. Belongs to the SsuE family.