What Ramses said.
The problem is that in a combustion chamber (1) the gas temperature is very high but the amount of heat is pretty low and (2) gases loose heat to their container very quickly.
You chamber might have a gram or so of gases heated up to 2000C but the gun itself is much more massive than that. You can do the full heat conservation calculation but you can get the idea if you assume that both the gun and the gases have the same heat capacity. Heat capacity is how much heat energy it takes to heat (or cool) a given mass by one degree. One gram of gases at 2000C versus 1000 g gun at 22C. Final temperature of the gun and gases is about 24C, which you can't even detect with your hand. And, that happens very quickly.
If you put a check valve between the chamber and a gauge what are you actually capturing? Combustion gases (that are hot and will cool) or air in the lines (which is heated by compression but will also quickly cool) or some of both? How fast is the check valve? Can it open/close fast enough?
It is easy to detect that the pressure spiked. Measuring the actual peak is a lot trickier.
