When my aunts and I did this 60 years ago, we never worried about the backs. We allowed knots to show. We were just careful not to run a long line of thread from one area to another. If it was far, we knotted and started over. If it was closer, we might loop the thread around other stitches in the back to travel to the next area. I have some of these stored away, but have never figured out how to post photos here. If I have some time I might try to do it later this weekend.
One reason not to run long lengths of thread on the back is that the flour sacks tend to shrink a little when washed. I don't remember what we did back in the day, but I would be sure to pre-wash the flour sacks before doing all that embroidery. It's probably a good idea to starch them after washing too. We used an embroidery hoop while working.
Again, I don't know about the old days, but the flour sacks I find locally in Fleet Farm, Walmart, etc. are often not cut and hemmed on the grain of the fabric so they wash and dry "wonky". It might be worth buying better quality flour sacks online -- the ones that are made specifically for hand embroidery. They may not be perfect, but might be better than the cheapies I am familiar with these days.