Everything we do goes back to horsemanship and keeping your horse really broke, and the start is no exception.
My secret to a great start in breakaway roping (and any kind of roping, for that matter) is training my horses to really score and react off my hand. Very generally, you let the calf make the first move, then you and your horse move. Because the length of the score and your timing leaving the box varies from situation to situation, your horse has to be on the bridle and listening to your hand and feet to know when to leave.
If your horse isn't responding properly to your hand, i.e. when you pull he pops up or tosses his head, you aren't going to get a good start. Your horse has to be responsive to the bridle, otherwise he'll pop up when you pull on him. That will take away that good, flat start you need.
Teaching your horse to leave flat off of your hand is key. In the practice pen, hold your horse still. Hold him with tension on the reins so he's on the bridle. Then, drop your hand really quick and squeeze with your legs, teaching him to move forward off of those two important cues. If you'd like, you can do this exercise in a corner to simulate the feeling of being in a box, but anywhere will do. When your horse is really listening to those two cues, take that work into the box and do the same thing.
Sometimes in the practice pen I like to let my horses start to walk forward slowly out of the box, then as the calf leaves I drop my hand and squeeze my legs, cuing my horse that he can then leave hard. That forward momentum you get from allowing your horse to start walking in the box keeps him leaving flat and moving forward.
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