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Ha, I also have some peanut butter in my... er... Emergency bag I guess. I had one before I even really knew of the whole bug out bag thing. My family called it a "Fire Bag" just in case we woke up and found the house on fire and what not. But yeah, the phone is a good idea, I can't imagine why anyone would think otherwise.
OP, great choice of multitool and folding knife. That bag isn't a bad choice either. I assume you've compressed that toilet paper? That would obviously save save. Also, ditch the box, and put the cliffbars either in loosely, or inside of small pot, which I also suggest. Something like a billy pot. To boil water, make tea, cook, etc. Leave the cliff bars inside that to save space. I would also add some way of wood processing. Could be a hatchet, small axe, or makeshift froe (large fixed blade knife made of 1095 Carbon Steel). I cannot stress enough how important a wood processing tool is when /out/, even if it's just a day hike.
What I am surprised about is OP's only fire making tool. I also have a zippo, in my pocket every day. But you're going to want more than one way to make fire, especially if it's only a zippo. Get a firesteel, like a Swedish Light MY Fire, or a Strikeforce. Having more than one way to make fire is important when camping. Cause our zippos run out of fuel pretty quickly.