Kits for natural disasters should be geared to the environment you live in. What you would have living on the coast of Florida would be different than the mountains of Wyoming. The items I feel are critical for the home, no matter where you live:
Weapons. Police and first responders will not be able to respond due to closed roads ( Hurricanes, tornadoes, flooding, downed power lines, avalanches, blizzards, etc) and other more serious problems.
A portable generator for an alternate source of power to the fridge, freezer, and coffee maker. I once went 7 days without power and making coffee only on a gas camp stove gets old. If you are not an electrician, have one come and put in a separate plug on your power box. This saves time and all you have to do is crank the generator and plug in, don’t do the “direct wiring method” unless you are an expert.
A reliable portable gas stove and spare gas cylinders.
A chainsaw, fuel, and chain bar oil.
A 16 to 20 foot aluminum ladder.
100 feet of nylon ski rope.
A good ax and sledge hammer.
A large medical kit and the appropriate training to use it.
If you have a fireplace, an adequate supply of cured wood.
If a family member has to take prescription medication to remain breathing, at least a 30 day supply.
A month’s supply of baby wipes, anti-bacterial gel, toilet paper, paper towels, paper plates, plastic spoons and knives.
Two week supply of bottled water and remember you need enough to flush the commodes. Average human consumption is around a half gallon a day (if in the desert, up it to a gallon or two)
Two week supply of food that doesn’t include Doritos or alcohol.
My everyday EDC that I carry on my body:
Handgun, one spare magazine, knife, very small flashlight, butane lighter.