Purchase one or more pairs of knee socks in plain white (preferred) or in a solid color or argyle pattern that complements the tartan of the dancer's kilt. The socks are worn just below the knee so get them long enough to fold down into a 1- or 2-inch cuff at the top.
Buy one package of 3/4-inch (child) or 1-inch-wide (adult) white elastic. Purchase 1 yard of 1 1/2-inch-wide grosgrain ribbon in a color that picks up one of the tartan colors in the kilt. A darker color will show up better against the white socks and is fine to use with darker or argyle socks.
Measure the calf of the dancer just below the knee with a tape measure. Cut two pieces of elastic to this length. For each piece of elastic, stitch the ends together, overlapping slightly (no more than 1/2 inch) and tacking any loose ends down. This can be done by hand or on a sewing machine, using a straight stitch.
Cut two 6- to 8-inch lengths of grosgrain ribbon to make the flash for a child's highland socks. Use an 8-inch length for a tall child and an 8- or 10-inch length for adult socks. Fold the ribbon in half and clip an inverted "V" in the free ends (not the fold). The "V" or notch should be about 3/4 inch to 1 inch long at its peak.
Slip this flash over the elastic so that the notched ends are evenly matched or the back of the ribbon is just slightly longer than the front. Sew the ribbon together right below the elastic, creating a snug "sleeve" for the elastic to run through. Do not tack the flash to the elastic.
Slip the elastic garter, with the flash sewn on, over the knee sock to within 1 or 2 inches of the top. Fold the top of the sock down to make a cuff, hiding the elastic. Be sure the flash shows below the cuff on the outside of the calf. Tack the cuff of the sock down with a stitch or two if you want to be sure it stays in place during a vigorous Highland fling. This tacking can be clipped, and the garter and flash removed when the socks are washed.