When I hike in the mountains, I carry a small pack with a kit of fire-making items, and a smaller, pocket-sized kit. The photo below shows the pocket case I mentioned in an earlier post, with the contents. There is a ferrocerium rod with scissors blade as a striker, jute twine tinder, a balloon tied shut with five waterproof matches inside, and a brass tube of lighter fluid. The matches in the balloon are waterproof, but the striker is not, so it’s all in the balloon to make it waterproof. I chose the bright orange balloon for visibility. The case is made of canvas so I could burn it in a real emergency.
Here is a smaller pocket kit. The case is a length of tubular nylon webbing, sewn at the bottom and with the top cut and folded to make a foldover snap closure. You are limited by the capacity of the webbing, so it holds less. No matches in this case, but it has the ferrocerium rod, some short pieces of wax-dipped jute, wrapped in waxed paper (the waxed paper can be used as tinder), two of the larger jute-and-tissue tinders, and a tube of lighter fluid. Another piece of folded waxed paper is tucked in behind the smaller jute tinders, just because it folds flat and doesn’t take much space. You won’t be using the case as tinder since it’s nylon, but it is a visible red color
Finally, here is the larger kit that is in my pack. The orange waterproof match case contains matches and has an Exotac striker strip on the inside of the lid. The yellow case has some Zippo waxed tinder sticks. The Ziploc bag has two Coghlan’s firesticks and some wax-dipped jute-and-cardboard tinder. The pill bottle contains four Coglan’s hexamine tablets. There is a canning jar lid to provide a flat, dry surface to light tinder, and some alcohol wipes. A Bic lighter and a Swedish Firesteel ferrocerium rod complete the kit. There is a mini utility knife for the Firesteel, as well as the original striker that came with it. This all goes in a zippered cloth bag.
You could make this smaller by discarding the Zippo tinders or the plastic bag with the Coghlan’s firesticks and the jute tinders. It’s really unlikely that in a lost hiker situation you would need both. You could shrink it more by discarding the waterproof match case, which holds something like 20 matches, and replacing it with some matches in a balloon, like in the first pocket kit I described. It’s all a matter of trading off what you are willing to carry against what you might need if you get lost. I’m still tinkering with what I carry, and I may replace some of these items with fatwood tinder or pack less of something. I don’t like the pill bottle for the hexamine tablets since it is larger than the waterproof cases for the matches and Zippo sticks. But unless I crush the hexamine to powder, the tablets won’t fit in anything much smaller. I don’t want to discard the hexamine entirely as I can use it to boil water or melt snow using my stove.
If you don’t want to take a pack when you go on short hikes, or you just think all the stuff in the larger kit is overkill, the first pocket kit I described would be adequate for most situations. As long as you can find dry wood, you can start a fire, multiple times, with what is in that kit.