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Can I modify the lookup table to define the most likely flow direction?
The GRID function FLOWDIRECTION creates a grid of flow direction from each cell to its steepest down-slope neighbor.
If a cell has the same change in z value in multiple directions, and is not part of a sink, the flow direction is assigned with a lookup table defining the most likely direction. The lookup table used by the function is stored internally; thus, you can neither see nor modify this lookup table.
For more information on the lookup table, see Greenlee D. D. 1987, "Raster and Vector Processing for Scanned Linework, Photogrammetric Engineering and Remote Sensing." Vol. 53, No. 10, October 1987, pp. 1383-1387.