In short, yes you are right. I considered the same thing as a child, your son is clever to be asking it even if he is wrong.

Mirrors do not reflect 100% of light, a small amount is converted to heat, also the light would heat up the air inside the flask. This slight loss of energy would eventually rob the light of all of it's photons- considering how quickly light would bounce around there would be none left to 'escape' when the flask is opened.

An interesting experiment is the opposite. Your son might like it. Take a matchbox. Colour the side of the drawer black. Then take a pin and punch a  hole. No matter how black you colour the drawer, the pinprick will allways be blacker. This is because the light that falls on the black colour is always reflected (that is why you can see it), the light that goes (through the pin hole) into the drawer is more or less trapped. You are actually seeing the absence of colour. So the light is trapped. Just like it would be in the question your son has asked.

Well Tij,

You are of course right about the light being trapped, but the way you say it makes it sound as though you could open the matchbox and let the trapped light out, whereas of course, it is very rapidly absorbed in the trap and converted into heat and chemical energy!

An interesting point is just how quickly trapped light will vanish.

Suppose you shine your light in a reflective sphere 3 metres in diameter. Suppose its reflectivity is 96% (which I doubt is possible in practice!)  Then the half-life of your light would be about 17 passes, taking about 170 nanoseconds. If you started out with the flash of a nuclear bomb (and a very, very strong, heat-resistant  sphere!) you would hardly get any light out if you opened your sphere after 1 second (about 5 million passes!)