Seems to be some confusion here:
The first and last posts before this seem to show a flat-twin 10 h.p. Douglas made by Douglas Bros., of Bristol (England) in 1913-23 whose main claim to fame was their flat-twin motorcycles.
However, Otto, you said it was not British or even European.
The Douglas Motor Corp. in Omaha, Nebraska (formerly Drummond) doesn't seem to have built anything small and so far as I know had no connection with the Brothers from Bristol.