For a fence to be useful, you need a truly square and parallel sided workpiece with very tightly controlled dimensions. Flipping the part doubles any positional error in features machined on one side versus the other.
If you can, it would probably be better to drill two dowel holes (on a wide spacing as practical) before the initial setup is disturbed. Then, make and use a jig plate with matching dowel spacing. The jig plate uses the hole locations as datum, not the edges of the plate.
Then, the program for the second side also makes use of the dowels as datum, rather than the edges of the board.