If I understand this situation correctly, the problem stems from an inaccurate reference surface. Bar stock is never truly square, parallel or straight, unless you pay extra for those features. Extruded square often has a belly to it, and it can tilt in the vise.
Depending on the precision you need, you might get away with marking one side as reference against the fixed jaw of the vise. Then, don't flip the part, rotate it so that the marked side stays against the back jaw. This will require reprogramming the operations on the second side because left and right have now been reversed.
Even doing it that way may result in a slight mismatch of features on opposing sides, because of the way that jaw/work tilt can creep in.
The best way, if you can spare the material, is to face at least one side of the stock so that it will sit reliably against the fixed jaw of the vise. Use two parallels under the stock so that you can test for proper seating of the part. Both parallels should be tight when the stock is tapped down with a dead blow hammer.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)