Your 100% Cotton fabric will wrinkle badly each time it is washed. Also as you sit in it, move, or breath.

I edge stitch all my Cotton Kilts. In you picture you will need to edge stitch at both the "Out Pleat" (Blue circle) and the "In Pleat" (Red circle).

Keep your stitching between 1/8" and 3/16" from the pleat edge. Use a fairly loose tension and a rather long stitch length.

Use only a good quality thread. Cotton thread will shrink on repeated washings. Polyester will not.

You must edge stitch your pleats prior to assembly. This means laying out your pleats very carefully and ironing them. Then edge stitch. Then baste the pleats into their final position.

You can choose to end the edge stitching at the Steeking line or run them all the way up to the waistband. However if you edge stitch all the way up you need to plan and iron in the correct taper before basting.

I find box pleats do not hold up as well as knife pleats on non-Wool fabrics. Cottons are generally lighter than Wool as well so the swish factor is cut down. In most Cotton Box-Pleats I find that after a while the pleats will tend to splay.

The secret is good Steeking.