I'm wondering if a barbarian with pouncing armor and an ability score of 17 in athletics can feasibly jump over a monster to reach the monsters behind as part of the charge jump allowed by the pouncing armor.
No. The problem is you can't get enough loft to avoid an opportunity attack (why you're trying to jump in the first place).
To get the distance you clear vertically, you divide the check by 10 and add two. Your maxium distance cleared vertically is 37/10 + 2 = 5. This means you are 1 square above the ground, that's enough (if you get a 13 or higher) to clear a short medium monster, but not enough to avoid an opportunity attack as you move past.
If you're looking for monster avoidance, the L2+ neck slot item Badge of the Beserker is the proper one. Pouncing armor is either to extend your movement (your max range becomes 7 here), or to reach a lowish flying enemy (prepare for a fall though).