How can I keep the cheese from leaking out of my cordon bleu during cooking?
The most common reason for leakage with Cordon Bleu Chicken is that the packets are too thick, which makes it impossible to get a perfect fold; you need to pound the breasts very thin - less than 1/2", maybe a little more than 1/4".

The other "trick" is to make a small cut along the folded edge of the breast after you fold and seal the packets, which essentially makes it almost like a sandwich; the top and bottom parts can move independently and you don't have tension trying to pull the top piece away.

Just don't cut so deep that you cause an immediate leak; if you've pounded the breast to 1/3" thickness, then your cut should be no more than about 1/8".

If you do it this way, you shouldn't even need to use toothpicks; I never do, and I haven't sprung a single leak in my last 20 or so preparations.