Wrapping around a zip tie huh? Thats new to me, I usually use screwdrivers or drill bits...something completely round. The flavor wick in Kanger coils is the extra wick on top of, not through the coil itself. When you take apart the dual coil you'll see there's 2 wicked coils with a loose wick between them. Single Kangers have a wicked coil and a loose wick on top of that. Since there's more vertical room in the dual coil housing, what I meant by fatter flavor wick is using a thicker piece of cotton on top of the rebuilt coil, to prevent flooding, gurgling or spitting...if you've only ever seen the new enclosed style coils it may be harder to picture what I mean than if you have seen the older style exposed wick coils. Do some searching around, there's many many videos and guides to rebuilding Kanger coils that include pictures, a whole bunch on this site alone, that will make things much easier and is how I learned to do it myself last year.
Also, it sounds like you're using a bit too much cotton for the wick through the coil itself. You want some resistance when threading it through, but not so much that it deforms the shape of the coil. Less is more through the coil when it comes to cotton, practice makes perfect and you'll eventually get a feel and an eye for it. Do some research and try to emulate some of the guides out there, rebuilding the Kangers is great great value and getting the technique down on the small heads will give you a running head start should you ever get into RDAs!