I agree with everyone's replies but I would like to add this simple suggestion: please consider your children(s) mental prepping for the next emergency. Most families have the general necessities covered, water, food, shelter, clothes, warmth, even some olives or toys, but rarely do we stop and think about what our children will be feeling at the very moment we they have to grab their "BoB" and run!
Children are more susceptible to stress and may freak out when things go bad. This is particularly worsened if you have a special needs child. It is so very important to give the child a focus that they can use to keep calm even when there is a lot of chaos going on around them.
The best way to avoid screaming children at a time when you really need them to stay calm is give each child in your family/group one singular responsibility. For example, my son is "in charge" of heat and my daughter is "in charge of morale". My son has learned several different ways to start a camp fire, he's versed in all fire safety and has even presented (of his own choosing) a report at school on the importance of staying warm and dry during emergencies. My daughter is a very bubbly person and very sweet. She is also an "Aspie" (Autistic Spectrum, high-functioning) and she was put in charge of morale because, as she says "it's important that everyone smile... A lot!" She has playing cards and puppets in her bag and she is in the process of learning a lot of jokes and shadow puppets.
Both of my children are totally vested in their responsibility and when we have our drills, they take them seriously. My son has even gotten to insisting on coming with me to the store when I go to buy more fire wood for the fireplace. "Mom, that's MY job!" LoL
The foundation for all this is simple though: my children have something to focus on if anything "bad" were to ever happen. I can confidently say that if I turn to them and tell them to get their things they won't be running around screaming in pure fear because all I have to do is ask them to "help me with your chore"...
This might seem like a mental trick, but it's really empowering your children and preparing them mentally. The rest is easy, just pack their bag just,like yours, but in mini size.
PS: I would have them help pack it, so it becomes "theirs". You'd be surprised how territorial they then get about keeping it clean and ready.

Hope this helps. Sorry so long.