It was indeed a design from Frits van Koolhoven and built by the "Nationale Vliegtuig Industrie". The National Aviation Industry was founded by Wallaardt Sacré, a Dutch army officer with the help of Vickers. In 1922 Frits van Koolhoven joined the NVI after their original designer Joop Carley resigned.
Like many of Frits Koolhoven's designs the FK.31 was received very well, but soon turned out to become a disappointment. The Finnish Air Force ordered 12, but the aircraft wasn't very well received by the pilots and the 12 aircraft only made 6 (!) flying hours. As the NVI encountered a lot of production problems with the FK.31 the development of the aircraft was abandoned.
In France a single prototype with a Gnome et Rhone 9Ac engine was developed, as the De Monge M.101 C2. But the aircraft was not taken in production.
Lefty, thanks for bringing another odd Dutch design under the attention. The model clearly shows the hand of Frits van Koolhoven and looks very much like the BAT FK.23 Bantam by the same designer.
Cheers,
Huub