Has anyone built an aircraft with a flat ring wing?
George Kitchen patented a design and half-built a biplane. It was completed by Cedric Lee and Tilghman Richards in 1911 but failed to fly. Richards went on to develop a series of increasingly successful Lee-Richards annular monoplanes before the outbreak of WWI.
This was a serious and promising design, having been wind-tunnel tested by the National Physics Laboratory in the UK during development. Kitchen and Richards understood that the strange shape would create vortices which trailed back over the rear part of the wing, and they used these to help impart stability. The monoplanes were indeed all safe and stable in flight (although the first was tail-heavy), a rare characteristic in those days. Pilots included Gordon England, Gordon Bell and NS Percival.