Maybe if you understand the mechanics of a lead change a little better you might be able to put things together.
Flying changes are a Lateral, much like sidepasses, leg yields and hip arounds.
More specifically, Swaps are the same type of lateral as a half pass. Bend to the inside, lateral motion to the inside.
Another thing... a horse picks up the lope out of the trot w/ his hindend first. Hence a lead change has to come from the hindend first.
Yeah, they can do it from the front to the back, but that will usually involve two lope strides. A correct swap is on one jump, hindend first and the front end goes w/ it.
The reason your horse won't swap on the back is cause he can't move his hind end laterally at your command.
Work on the laterals, specifically, get him to move his hind laterally, and you should have better luck.