Moisture condensation usually accumulates in the bore, mouthpiece, and especially in the SAC (Slow Air Chamber). Moisture dries fairly quickly in the bore because of its size and the amount of ventilation. However, the SAC is more enclosed because of the plug, the silicone band, and because the mouth piece is somewhat narrow.
After playing your flute, simply move the silicone band (fetish) up a little to expose the top air hole. This will allow more air through the SAC and will dry it out.
Having said this, there really is not much to worry about. The inside of the flute is finished with epoxy that protects the wood itself from moisture.