Hard to say exactly how much pressure. Try putting an indicator on it and torque it until you see movement.
Generally putting the stock lower in your vise jaws will yield less bending, especially if the bending is upward. In some cases, vise jaws like to tilt back, lending to the force being applied to the lower part of the plate, causing it to go up.
If you can't handle a vise making it go up, just toe clamp the thing to a sacrificial subplate/piece of material.
Not-even-that-old-school technique: Holding 14x18" in a vise? Forget that. Use strap clamps and clamp it to the table (or precise blocks placed under the strap clamp contacts). If you need to machine the entire top surface, clamp part of it, machine the other part, clamp the machined portion before removing the original set of clamps, remove the original set of clamps, machine the remaining part. Manual, you know when to switch clamps. CNC, create an appropriate tool path and put in an M01 when it's time to switch clamps.