I would just run them under the tap. Turn the water to about mid way pressure then hold the coil down low in the sink and let the water blast through the middle. Then rotate it to the exposed wick bits on the sides and just let the water blast it.
Sadly the coils are really sealed up so getting them apart like the pro tank 2 to get at the wick and coil is difficult.
When i was using the PT3 / AeroV2 I found it easier to just replace the coils sadly. Though i suspect that was their plan all along. People were rebuilding the pro tank 2 coils and never buying replacements. so they saw to that.
Looks like its time for you to get into dripping. Or at least rebuildable tanks. (kayfun / russian and the likes)
-Crit
EDIT: I just dug into my box and dug out one of the pro tank 3 / aero tank style dual coils and tried my hardest to get inside. Destroyed the threads, knackered the post and tube and she still wouldnt give up her secrets just to be sure they they had in fact created a sealed coil... Sorry man. There is no getting into these that i can see.