The arm in guillotine is my favorite guillotine. I like all of the control that it offers and it's great to chain with other arm in techniques and to sweep and pass. The finish takes time though and I haven't seen a lot of good videos on it online.
Let's say you're choking them with your right arm. One thing you really want to do is keep your left elbow tight to your side. It keeps their trapped arm close and keeps their elbow open. Anytime their elbow is open they are pretty weak and that means your own elbow is close to your side, which makes you pretty strong. If you're attacking the choke from the front headlock or something and you "reach in" too far and open your elbows up you could end up in trouble.
When you finish the choke, much like other guillotines, you want to be on your side and not flat on your back. Instead of arching back, do a side crunch as if you were putting their forehead into your pocket. So right arm choking, on your right hip, left elbow close, doing an oblique crunch, putting their forehead into your right pocket. You want to get the lower part of your forearm under their throat and actually you can even use the tip ridge of your wrist or even the top of your thumb. You can even use your right hip bone underneath your grip to reinforce it. You want it to feel very shallow. It should almost feel like their head is about to pop out and you should be able to see the lower half of the back of their head. It can be a slow burning choke and it doesn't tend to produce the fast taps that the high elbow guillotine causes. But it's very strong once you get the pressure down. Keep your far leg high up on their back in case they try to roll or flip out so you can ride to the mount.
This is probably the best video I've seen for the finish on youtube. Jeff Glover probably has the best arm-in guillotines going as far as pure grappling. He's great to watch for film study. Him, Murilo Santana, and Dillon Danis. Sadly I can't think of many more in pure grappling that use the arm-in guillotine all that much. The high elbow guillotine and some other no arm guillotine variations are sort of the craze now. Rightly so. The high elbow is awesome. Jeff Glover actually was all over the high elbow guillotine and then started working the arm-in also after looking at the benefits. Also check out Renzo Gracie or Joe Daddy for mma guys that have good arm-in guillotines.