Crossfiring, cross cantering....same thing.
An exercise I would suggest is to lope decent-sized figure eights at a steady pace. You don't want to be rushing and strung out, but you need to have some impulsion. Set the horse up correctly at the start of the circle, ask for a lope, and lope the circle a few times on the correct lead, making sure the front and back are synchronized. As you approach the center of the figure eight, straighten your horse and bring him down to a trot for a few strides. Ask for the lope again on the new lead. If the horse picks up the wrong lead or is messed up behind, bring him back down to a trot, set him up, and ask for it again. Lope a few times around that circle, then straighten near the center and switch to the other side of the figure eight through another simple lead change. Once your horse has this down, start asking for a flying change at the center. If he switches behind, bring him back to a jog and ask again.
Hope this helps!