The images that can be found via search engines are mostly of nicely painted attractive young ladies, though he did make paintings dealing with landscapes, and it is mentioned here and there that he was a war artist (though I found no examples of that genre).
The link above and others say that he was influenced by John Singer Sargent, and a whiff of Sargent can be seen in his portraits of ladies.
To me, this doesn't look much like His Royal Highness.
Sketchy, incorporating a figure with the landscape.
Also sketchy, but here the figure predominates.
Another scene with nature.
Yet another painting with subject matter hinted -- but it's pleasing.
The subject's face is subdued, so Barnes seems to be trying for effect by using an apparently anonymous sitter.
Here composition dominates.
Simplified color areas, but not distorted, simplified shapes in the 1920s modernist fashion.
Another painting from the 1920s. Barnes had a nice touch with his brush.