Storage is somewhat easy…makeup carrying cases do well. They are sometimes called “train cases” and run the gambit in price from 30$ to over a 100$. These can be good for storage at your residence and some models are good looking travel bags hence the “train case” name. Some of them look suspiciously like fishing tackle boxes which reminds me…whatever you buy you can also get plastic cases with adjustable inserts to put into whatever bag you choose.
For carrying on your person I hear the tutorial covers a bit of that but I don’t own this product. But a stab in the dark…since the trick you mentioned uses fire maybe a matchbook or matchbox would work for storage, that would prevent you from having to go into a wallet or something at an odd moment. Maybe someone who performs this trick will chime in…
For carrying other gimmicks the ideas are plenty and without narrowing down what type of gimmick it’s just a broad smattering of ideas….arts and crafts provided some avenues. Old cards and deck boxes are useful, so is fimo clay.… film canisters are useful…different types of paper clips…
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Here< is kinda a cheap idea but you can see the plastic compartments I mentioned. >
Here< is a makeup bag that looks nicer for traveling and it has adjustable bits.