Hi Silverport,
No, it's not part of a rifle cleaning kit, but you are correct about the wick.
It's a tinder cord lighter.
Photos courtesy of Pete O'Keefe
The wick would drawn through the tube to expose part of it, then lit by a tinder box. The smouldering end would then be passed around an asembled party of smokers to ignite their cigars or cigarettes. When everyone was lit, the cord would be drawn back into the tube and the plug inserted to extinguish the burning end of the wick.
If I remember rightly, Postnikov has an example of a Russian cigar case with a similar form of ignition, hopefully he will see this and post a photo of his example.
The revival of this form of lighter during WWI was because of the danger of lighting cigarettes with matches often attracted the attention of snipers.
Trev.