Like someone else said, its just muscle memory. Luckily this is an easy move to practice. Figure out how many cards you are going to be using for this move (depending on the effect or flourish, you may have more or less when you reach the point that you need to do the Instant Replay move), and just keep breaking off that number of cards and flip it into the other hand.
Practice it over your bed, or while sitting so that clean up is really quick and just keep practicing. An couple of hours of this while watching a movie or something and you should see some real improvements. With any trick or flourish, its always a good idea to break it down into smaller parts and focus on each part one at a time. If your problem is just flipping that packet, then ONLY work on that don't worry about the parts before or after. Dedicate some hours to just that one move and eventually it will all come together. I hope that helps a little.
Victor Cruz