I recently had a flat tire myself and got an embarrassing reminder of my own car preparedness. - The cup set for unscrewing the bolts was in my garage. - The jack was in my garage too. - My spare tire, although not one of those accursed donuts, was almost empty of air. Fortunately the flat happened only a hundred yards away from home so I didn't have to stand there like an idiot calling in for the road emergency service truck. I learned though, and now all the necessary gear is well tucked away into the car.
The OTHER gear has been in place for a while though. Basic tool kit, emergency vest, emergency triangle marker, towing rope, big first aid kit, e-tool type folding steel shovel, and a kit set with: coins, matches, pencil, paper, sewing kit, micro flashlight, folding knife, some sugary sweets. And I keep a blanket in the car during the period when the temperature goes below zero.
But I don't have any emergency supply of gas, water or oil in the car, nor duct tape. I see the wisdom in this should there be an engine system breakdown on the road and will get a couple of each to stow away inside - thanks for the tip. And I need to find a place for an extra set of charging cables too. As the man said... Winter IS coming.