Plain old backward loop cast-on is often what's used for double knitting. Be sure to cast on enough stitches for BOTH the front and back of the work (basically, twice as many stitches as normal, or twice as many as shown in your chart).
Does that answer your question?
KnittingHelp Queen Bee
It is not because things are so difficult that we do not dare; it is because we do not dare that they are difficult.