What are the uses for 'quick'?

Is the word quick ever used in reference to candles eg the quick of the candle? I know about the quick of the nail and obviously about the wick of a candle but I have a memory of the quick too being something to do with candles.

Only metaphorically. Quick means either "with high speed" or "alive", the latter being a somewhat outdated usage. One could imagine some poetical description of a candle flame being alive.

The flame burned, consumed the wick,
As if the candle flame was quick.

(Ok I'm not a poet, just an example... :-)

More likely you heard "wick" rather than quick.

Google finds only 9 instances of "quick of the candle", and one of those is this question!

Quick in these instances is clearly an eggcorn for wick—

In linguistics, an eggcorn is an idiosyncratic substitution of a word or phrase for a word or words that sound similar or identical in the speaker's dialect. The new phrase introduces a meaning that is different from the original, but plausible in the same context, such as "old-timers' disease" for "Alzheimer's disease". —Wikipedia

The original meaning of quick was “alive, living” which evolved quite naturally into “lively” and thus “fast”. The original meaning has almost disappeared, except in such fixed phrases as cut me to the quick (that is, to the ‘living’ part of my flesh) and the quick and the dead.

I don't recall hearing that phrase but it might be related to quick meaning alive ie the candle is lit.