I built and fired a small salt kiln in grad school that was big enough for one 12x24 in shelf- 27 inches tall with 27" x 22.5" interior. It was a simple cross draft with a hole in the top corner for an exit flue, and one power burner. The top was kiln shelves covered with firebricks. It fired like a charm and gave great results. But even that little kiln, which I wouldn't go any smaller than, took 500 bricks.
I was reading Phil Rogers book, Salt Firing, and he tells a story of Walter Keeler, renowned for salt firing, building such a small kiln in about an hour. Seems Keeler had agreed to sending pots to the Victoria and Albert for an exhibition but had no salt kiln. The small kiln was large enough to fire six tall jugs. (see pages 163/164 for the story). Rogers also has the plans for a ~500 brick small salt kiln, about 12 cu.ft. in the book (pages 68 to 72), including materials list. [Cue the rush to Amazon to order copies of Phil's book).