I work for Teledyne Isco, which makes the CombiFlash systems. "CombiFlash" chromatography is just flash chromatography run with a CombiFlash system.
Although, as an employee of Teledyne Isco I would like scientists to use our systems and columns, most purifications can be done using the same method with traditional flash chromatography.
The CombiFlash system combines a UV (and other detector types) with a pumping system and fraction collector. The system allows walk-away automation and frees the scientist for other tasks during the purification. The machine- packed columns allow purification of closely eluting compounds, an advantage over hand-packed columns.
Essentially, CombiFlash chromatography is just automated flash chromatography.
For more information, please see: http://www.isco.com/