2 issues here with the materials....
1) natural fiber rope/twine is commercially made. The fibers are grown and harvested, but during the growing process they are treated with insecticides and herbicides to insure a good crop, and then it is treated with chemicals to retard rot. All those chemicals are in the smoke given off when it burns. I know it's not a lot of material to burn, but I don't use this material for fire starters for this reason.
2) the man made fibers of dryer lint is also toxic. One must be assured there is none present in the lint. In order to insure one has 100% cotton, get an old t-shirt and scrape lint off it with the edge of a knife. It's a little more work, but as we all know, the boys are WEARING all the "dryer lint" needed to start a fire.
Then there's the issue of char cloth. One doesn't need a large can to pull this off. A small shoe polish can works just as well as does any small seal-tight tin/steel container.
I always just use the candle stubs from tapers. Usually they get thrown away with at least 2 starters available. The nice thing about them is they are 100% waterproof. While they won't take a spark to ignite, I always duct tape a couple of them to my waterproof matches container. Birthday candles work well, but do not have the burn length necessary to get wet wood going.
Sequoia trees grow to such huge heights because the sap they produce is not flammable. When fire is around their base, the sap leaks out from the fire and extinguishes the fire. The sap of other pines is more flammable being a turpentine base.
The most valuable tree in the forest is white pine. I teach my boys that stick matches are made out of white pine. They all know this and carry a 6' walking stick with a hook on the end as part of their gear. The dead lower branches are the best fire starters out there. Whereas all the other troops have cleaned out all the easy branches on the bottom, the hooked stick can reach up an additional 6' and so they never have a problem with an over camped area. If it's raining, I have the boys cut off the wet bark and use the dry wood within. Like stick matches, it does catch and hold a flame with no problem. If a spark can light a match, a small pile of leaves or pine needles will burn long enough to ignite white pine. Otherwise a sparked char cloth will produce a small flame necessary to get the white pine going. A magnesium burn only lasts a few seconds, but it's long enough for white pine. Did I reference white pine enough? For heavens sake, a Bic lighter will ignite a small white pine stick (about the size of a match long enough too. That way one does not need to hold the Bic down into the fire lay. Remember the average sized Bic lighter is the equivalent of a quarter stick of dynamite.
I have my boys make their own fire starters out of paper egg cartons. Fill them up with lint or sawdust and drip paraffin on top to hold everything together. When need, tear one off (the ragged edges make the wick and will burn for quite some time. In case one has done the math from above, white pine sticks dipped in paraffin make a great fire starter too