I had an annoying click on my singlespeed that only mannifested itself when pedalling. I stripped an greased everything and then eventually narrowed it down to the rear brake calliper.
It appeared that the when putting force through the drivetrain, something must have been catching on the rear brake which caused a metallic like click.
I took off the caliper , cleaned it, replaced the pads, centered it, and the click stopped.
It took me ages to find as I was convinced it was coming from the crank or seatpost area due to it only happening when I was pedalling.