All the above steps are awesome, but if you are just looking for quick fix that you can do now, then just blow them out and dry burn. I never have a problem with flavor creeping and generally go from flavor to flavor without blowing out. Now, some flavors are notorious for hanging around in an atty for dear life, and then I would suggest the above steps, or....
I have tried several methods all with little to no avail to get the stubborn flavors out. Yesterday I boiled my attys, that may make some people cringe, but it worked tremendously well and my attys are like brand new (minus the break-in phase). I boiled them for five minutes, then rinsed them out and repeated a couple more times. Then, I blew them out thoroughly making sure to get as much excess water out as I could. I let the attys dry out in the sun until I noticed the wick get tight and dry looking. Next, I brought them back in the house and left them near an open window for the rest of the night. This morning I was completely
thrilled to have great working attys again with zero previous flavor or smell.
Amendment: I am using standard Joye 510 attys. I would not recommend boiling or any other harsh method with any atty that is on the more expensive side. Check out the vinegar and baking soda method as well, it may work for you, but it didn't work for me.