I have flown with a staff and wicks in my bag (not carry on obviously). I would assume that you wouldn't be able to carry fuel unless you managed to organise it in advance, but with a normal commercial ticket I would guess it's impossible.
The rest of the kit I don't think should be too much of a problem. Provided that it is all in a bag which is secure and safe, always best to check with the airline first though. Wouldn't want the kit to have to stay behind.
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If i had a world of my own, everything would be nonsense. Nothing would be what it is, because everything would be what it isnt. And contrary wise, what is, it wouldnt be. And what it wouldnt be, it would. You see?