Flat-coats were fairly common on Victorian postcards. Here is a sampling.
This beautiful card is from 1918.
Hard to tell if this dog is really a flat-coat, but it looks close enough!
A very appealing card from 1920.
A Victorian fringe card with a rather odd portrayal of a flat-coat.
A very attractive sepia-tone card from 1940.
This card is from approximately 1908.
A cute Christmas card from the 1920's.