When you run down the hill, just before the bottom are two barrels of napalm. Your buddy AI guy will run to the left one. You have to get to the right one, and hit X. You stab the napalm, spark it, and then roll it down into the bottom to blow up. Then find some cover till you get your next checkpoint. Then just follow the map some more, then go up a hill, and mission is done.
Actually, there are two napalm barrels that you have to stab/kick. After that, you get a checkpoint. You can kick the further one to the right first, that will make you get a checkpoint sooner then you can come back to the other one.