The chemicals used in these devices are relatively stable, if stored under the
right conditions of light, temperature and humidity. Also please note that
typically these pyrotechnics are packaged in individual sealed metal
containers, inside sealed waterproof wrappings.  However, they do represent
serious fire hazards, due, particularly, to the white phosphorus which is a
basic ingredient of many of these items. This is why the military tends to
segregate these from other stored items, often keeping them in separate
"dumps".

I suggest treating it as ammunition.

With the exception of a small quantity of blank ammunition and black powder
used in re-enactments, we store all such materials off-site, at a licensed
range's storage facility; if I had any pyrotechnics (which I don't), I'd store
them there as well.

Harry Needham
Canadian War Museum