Ardent got it right, it's really up to you. I rarely rinse mine out between flavors.
Now if you are sampling and want to see which ones you like, you can give it a quick rinse in hot water and blow out from the battery connector into a paper towel. Some people also like to drip a couple of drops of pure VG in there and vape that to really get rid of any left over flavors.
When you see a difference in flavor or vapor you can also soak the whole atty in some everclear or vodka for a few hours, give it a rinse in clean water, blow it (from the battery connector end again) out and then vape.
Just a word of warning, these attys don't like to be dry when you put them away - so drip a couple of drops of liquid in there if you are going to store it.
Enjoy the world of dripping, it's where the flavor is at.