We have used occasions like birthdays, Christmas, etc. to give our children gifts of flashlights, headlamps, books about survival skills, pocket knives, sleeping bags, and other outdoor gear. Yes, they also get toys like other kids, but usually we're able to slip in some preparedness gear as well.
Then, practice using the preparedness gear with your kids. Their gear and yours. Don't lock it up somewhere "safe" and never use it. I'll be honest with you here, sweet husband is way better at this than I am. He welcomes and encourages help from the kids even when it slows him down. He has been known to put a child in charge of lighting the campfire with his flint and steel (with dad's help and encouragement of course) while I would have just lit a match and got the dang fire going. Son did get the fire going eventually though and what an accomplishment for a then 9 year old!
Our kids get to rotate through their own emergency kits, help light fires, use tools, and help with the planting, growing, harvesting, and preserving of the garden each year. They get to help me make meals and help dad fix wiring and pipes. They get to use their pocket knives, shoot the guns, and hammer nails into boards. I haven't started them on the sewing machine yet, but it won't be long. No, it is usually not faster or easier to let the kids help. And no, I don't always let them help. But I try. They are part of my team. By having the gear and letting them use it, we are giving them the tools and the skills they need to be a little more self reliant and more prepared which, in the end, will help us all.