Your not sweeping 3 strings in this, only 2
I haven't seen how Justin teaches this, but I would do it this way. I am assuming it's eighth notes.
Pick 12 hammer on to 14, pick has slight rest between G and B strings then sweep through 13 on B and 12 on E. Just practice that part over and over till smooth. All down strokes.
Now pick 15 on E string with upstroke, pull off to 12, pick has slight rest between E and B string, then sweep through 13 on B and 14 on G. Just do this half over and over till smooth. All up strokes.
Then join together. The hard part is finding the right muting technique to stop string noise. Use your neck pickup for a smoother sound.