The indexing of patents of that era is a little wonky on Google Patents due to OCRing from such old originals, but I’ve found these:
#1,801,656 Moving-picture film http://www.google.com/patents?id=GIFeAAAAEBAJ
#1,833,706 Apparatus for tinting motion picture http://www.google.com/patents?id=IHdUAAAAEBAJ
#1,859,021 Method of producing motion pictures http://www.google.com/patents?id=GH9tAAAAEBAJ
#1,859,022 Projection printing machine http://www.google.com/patents?id=GX9tAAAAEBAJ
#1,859,023 Projection apparatus for motion pictures http://www.google.com/patents?id=Gn9tAAAAEBAJ

They are all heavily focussed on the film layout with little mention to how background masking might work – but the last patent hints at how the projection might work. I suspect the intention was to have a semi-transparent front screen which the background was projected through. Each layer has a different lens, so they could focus at different depths.

It doesn’t look very practical to me though – focussing and alignment would have been a nightmare, you would need huge lenses to achieve that much depth selectivity from a distant projection position. Besides, the semi-transparent screen would introduce a lot of blur. The lenses need to be very close for alignment, but well separated for adjustment. It’s one of those things that works really well on a small bench, but probably didn’t scale to useful proportions.

Also…
How would you film anything?
Live action in the studio against black velvet?
Dozens of animators to make the mattes? (Like TRON?)

It’s only a method of storing 3D on film. The patent doesn’t explain how to produce the 3D illusion from the film. That appears to be Jacob Burkhard’s only patent – so I guess he never figured that part out.