johnston ,
A three ply Flemish twist string is made in the same manner as the two ply string, there is no braiding involved only twisting.
I think you are getting confused with the so called Scottish twist or Scottish braided string shown by some on this site where, if I remember correctly, the loop is twisted as in a normal Flemish twist string but the tails are what you would call braided. It is claimed to be a quicker thing to make, I have my doubts and also believe the braid would be too elastic and rob the bow of cast. Anyway back to your question I have only seen the "Scottish twist" done as a two ply but would imagine a three ply one would be done like any flat 3 ply plait, sorry braid.
Craig