Catalyzes the reduction of FMN to FMNH2 which is used to reduce pyrimidine by RutA via the Rut pathway. FMNH2 + NAD(+) = FMN + 2 H(+) + NADH Up-regulated by the nitrogen regulatory protein C (NtrC also called GlnG) and repressed by RutR. Belongs to the non-flavoprotein flavin reductase family. RutF subfamily.