Is it normal for drill bits to slip in a keyless chuck when binding in metal?
Yes. It's a common occurrence especially when I use a DeWalt keyless chuck. If the chuck is sized for 1/2 inch capacity it will happen more than 3/8 or 1/4 inch chucks (from my observations).
If I really need a driver or a bit to remain secure and the chuck to keep a solid bite I'll tighten the chuck with Channel Lock pliers or something similar. Grip the chuck with pliers and slowly press the switch until the drill is almost ready to leave your hand.
To facilitate the bit not binding just before it completes the boring task; apply lubricant just after you start the opening. It also helps to keep the bit at a 90 degree orientation (if applicable). Also drilling with the RPM's on 2 setting (fast), but intermittently pressing the trigger (goosing) will make it easier on the bit and the drill with less binding.