The Guillotine, in all of its forms, is my absolute favorite submission. The Flying Guillotine is especially great because, even if you can’t or have no intenion on finishing it, it is a great way to open your opponent up for a takedown or, at the very least, disrupt their rhythm and throw them off their game (at least for a little while.)
The best way to approach the Flying Guillotine is to first think consider your stance. I’m right-handed and primarily a striker - a Muay Thai guy - so I lead with my left leg. Many people from wrestling backgrounds will lead with their strong side, so right-handed wrestlers will often lead with their right legs. Whichever side you lead with, you’re going to use that hand to control your opponent’s head. For example, since I lead with my left leg, I use my left hand to control the head.
In either case, you place your “lead hand” on your opponent’s head as you’re leaping and push your opponent’s head down and over to the opposite side of your body. In my case, I use my left hand to push my opponent’s head down and then towards my right armpit. My right arm will then come around my opponent’s neck, with the blade of my forearm across their throat. As I land from my short leap, my left hand will come and lock up with my right hand. The most important thing here is that I don’t have an arm trapped. That’s going to make it more difficult for me to finish the guillotine and presents my opponent with more options for escaping. Once you’ve joined hands with the preferred grip (a ten finger grip for this variation,) you can pull either full or half guard - your preference.
The counter:
This isn’t really a “counter” in the traditional sense. The goal here is to react fast enough to avoid being pulled into your opponent’s closed guard (full or half) as that makes things much more difficult and really presents you with much fewer options.
What you need to do (and of course it always helps to drill) is; as soon as you feel your opponent’s arm come around your neck, you need to prepare yourself to react. Timing is everything for this counter.
If your opponent grabs your head and begins to tuck it under their right arm (which is generally what I would do if I were performing the move since I lead with my left leg,) you will need to escape to your opponent’s left side. If your opponent begins to tuck your head under their left arm, you will need to escape to their right. Whichever side you’re escaping to, you will need to wait until the moment your opponent starts to pull guard, at which point you will actually begin your counter/escape.
Rather than make this any more confusing, let’s just use an example. Your opponent has your head trapped in their right armpit. You need to escape to their left, so as they start to pull guard, you will use your right arm to hold down their left leg and you will hop your legs - one at a time, starting with your right - over their left leg. You should land in side control, but your opponent will most likely be holding onto your head for dear life. The best way to get it out is to wriggle and pull your head clean out. If you’re unable to free your head this way (which is very possible and probably likely,) you will need to use whichever hand is not under your opponent’s head to grab their wrist and pop their grip.