No. The wick isn't burning. The wick cannot burn. It's silica and silica doesn't burn. I chain vape with a Fluxomizer all day, every day and they wick fine. The worst that happens is when they get low on juice, I have to tilt them for a couple seconds every other draw or so. You can turn them upside down and they won't leak.
If you're getting a burning taste, there are only two possibilities. Either your juice is very thick or it's not wicking fast enough for some other reason, (my guess), or the coil is contacting the small inner lip on the underside of the silicon seal on top of the cup.(you'll taste a distinct burning tire taste)
The solutions are to do one or more of the following depending on whether or not you are tasting a burnt plastic or rubber taste. Before you do any of this, make sure the Fluxo is 3/4 full and tip it upside down for 3-5 seconds. Let the wicks soak for a couple minutes.
1) use thinner juice.
2) enlarge the notches on the silicone cap with an exacto knife or similar. Dont' make them longer, make the V a little wider so the wick is not restricted.
3) don't jam the drip tip so far down on the silicone plug. Don't push it down so far that it jams the silicone into the coil. The bottom of the drip tip should just barely touch the plug.
4) Push the coil down slightly if it is raised so that it doesn't hit the silicone plug.
5) Use a pair of small maincure scissors to trim down the small inner lip on the underside of the silicone plug.
6) Fluff the wicks. Use a small hooked device, or a paperclip or something to gently lift the wicks toward the top of the notches in the side of the cup.
7) Use a hooked device like a bent paperclip to lift the silicone cap slightly. It doesn't need to be jammed down tightly on the ceramic cup.
You won't have to do all these things. Try them one by one according to what is most convenient and makes the most sense in light of the specific problem you're having, either a wicking issue or a burnt plastic taste.