The Black Pirate was the third feature to be filmed in an early two-tone Technicolor process that had been first introduced in the 1922 feature Toll of the Sea. This reproduces a limited but pleasing range of colors. Ben-Hur— filmed around the same time — contains two-tone sequences but is shot primarily in black-and-white with tinting and toning in many scenes.
Fairbanks spent considerable money on color tests before making Pirate. Two-tone Technicolor at that time required two strips of 35mm film to be fused together back-to-back to create the two-tone palette. Due to the heat of the projector, there would be so-called cupping of the film, making it difficult to keep the film in focus during projection. (Technicolor later perfected its process, so that two-color films required only a single strip of film.)
By Albert Parker (YouTube) [Public domain], via Wikimedia Commons