Hello!!
I believe there is a medium flow nipple available for Playtex? But anywho
I always switched nipples when he/she seemed to be frustrated with it (pushing it away, drinking less, etc.) or when it started to take a long time to finish a feed. Though you can't really "teach" them how to go to a faster one, it may take a day or two to get used to. With my little ones, they choked/gagged a little bit during the first couple of minutes but then it got better. I would say though that if they are choking/gagging through the entire feed, he probably isn't quite ready. The other thing I did was poke a toothpick through the slow nipple to make the hole bigger, but not quite as big as the fast flow.
Good question on the tri-cut. I wonder the same thing...I was thinking it was for babies that need cereal in their bottle?
HTH