@StaffSlinger - That looks pretty awesome! I'm going to have to make me one of those.

@Deltafour1212 - This isn't really my forte. So forewarning, I could be completely wrong. I do braid slings, but I don't weave the pouches. I just use leather.
But here's what those look like to me. The cords are a regular 4-strand round braid. If you're not familiar with that, just run a search online. There's lots of tutorials out there. The pouch looks like a regular over/under weave around those 4 strands. The weave will be done in a similar way at this:
https://www.youtube.com/watch?v=s6EhnhCY_08. But in the linked video, he starts at the pouch because the cord needs to be looped back and forth to create the 4 strands. You won't need to do that because the braid itself is already providing the strands.
You will need to add a strand right before you get to the pouch to do the actual weaving. You can do that in several different ways, but the easiest is probably to add a piece of paracord along side one of your other strands for the last few inches before the pouch. Then you can just start weaving with it. And the same thing can be done on the other side of the pouch. Just braid with the extra strand for a short length, then drop it (you can just cut it off and melt it). Then braid the release cord to the desired length.
I hope that made some sense. It's where I would start if I was trying to duplicate one of those slings. Someone else who is more familiar with woven pouched may have some other ideas. Good luck with your investigation!