One thing I have found that helps with persistent clogged, 'burnt' wicks is to soak the unit in pure alcohol(ethanol). If you have something like a mini protank which has little coil cores then you can remove the core unit and put that in a clean old juice bottle with 8 ml of ethanol. Agitate gently and leave overnight.
The core can then be warmed to dry it and reinstalled into the tank. For non-core units just get the ethanol in the unit and soak the wicks and coils in situ. If you are concerned about residue (with pure alcohol there should be absolutely none) you can also rinse with water afterwards. I don't bother. I just don't inhale the first few puffs of a freshly-cleaned wick. Ethanol is safe to handle and will not damage the metals, glass, plastics, silicone, rubber or any other part of a tank or coil core.. Just use ethanol in a well-ventilated area away from sources of ignition.
If you use the juice bottle method then you can rinse out the burnt juice from a coil core with Silica wick very effectively without breaking the wick strands up and causing fibre release and without having the ethanol knocking around in an open container. I have been cleaning my wicks this way for years and I can vouch for how excellently it works. It is as safe as using vodka to clean your wick. You could even use Everclear or Polmos Polish spirit (80% alc.) . Any extremely strong, clear spirit can also be used for this. Even normal vodka although this will not evap entirely by itself. A few fires of the coil will soon clear the vodka.