You can use a technique called "Railroading" to prevent the floss from twisting!
Here’s how to do it :
Stitch by bringing the needle up through the fabric and pull the floss along the fabric in the direction that the stitch will go (so the floss is lying flat over the hole where the needle will go down). If the strands are not perfectly flat and parallel, give them a flick with your fingernail to smooth them. Then insert the needle between the strands (be careful not to split a strand) and go down to complete the leg.