When I think of a fish scallop pattern, I think of a running bond brick pattern. This may be what you are wanting instead of a stacked scallop design.
While I have not done these, I do see a way to do them.
If you already are using a cutting sled to cut the four flats, an additional jig needed would be a V cut jig to hold the blank on its corners while being cut creating an octagon Style scallop which should replicate the fish scales.
This jig can be made with two V cut blocks which will capture and hold the blank for cutting. Clamping sounds like a good idea.
You may need to adjust blade height and length of cut for scallop spacing to be uniform.
Good Luck and let us know how this works.....and perhaps create a tutorial too!