Personally I find a bit of condensation builds up in the chimney, so whenever I empty a clearomiser, I rinse it all out under warm water, wipe it dry with a towel, blow through the mouthpiece and coil to get rid of any drips, and put it all back together and refill. The first couple of puffs are sometimes a bit tasteless as I'm vaping the water that's in the wick, but then the flavour comes through.
You can just refill it with a new flavour if you like though, it won't do any harm.
Some flavours will cling, so you might want to keep a dedicated coil for those flavours to prevent any mixing. Menthol probably won't go great with coffee, for example. You might also stumble across some great combinations!