A* makes two kinds of chest protectors. There's a one piece:
And the two-piece inserts:
Generally, track riders just slip the one-piece in place under the suit, then zip it up. It stays in place due to its shape.
The two-piece fits into pockets in the jacket liner. The pockets you describe are not those. The pockets you've seen are for carrying loose change, etc.
If your jacket is like mine, the chest protector pockets are hidden inside the liner, so it's not surprising you've missed them. My jacket has no provision for the one-piece protector. There's a zipped access across the bottom of the liner, at the back of the jacket where your tailbone is. Mine's conveniently labeled "INSTALL PROTECTION HERE."
Open up that zipper and slide your hand up in between the liner and the jacket shell. Feel around in the chest area. You'll encounter some additional loose fabric and velcro tabs in the chest area, one on either side. Those are the pockets for the two-piece protectors.