Lucky me, I have 3 kids who are 23, 16 and 10 years old and they have never asked to get a tattoo. If you also believe your kids will never be able to predict what the future holds for them and would like to reduce the chances they will ask to get a tattoo, here is what I have done and I hope it will give you some ideas.
If you see a beautiful tattoo and you like it, say right in front of your kids that you think it is beautiful. Make sure you separate the beauty from the act of burning the skin. You do not want them to think you are old in your mindset and do not understand anything about beauty.
Let your kids express themselves. If they want to start putting makeup early, let them do it. Noff has had her own makeup kit since the age of 3. She used to go to daycare with her face full of lipstick (even as eye shadow). Makeup can be cleaned with soap, not with a knife.
Allow your kids to enjoy face painting everywhere they go. Learn how to do face painting yourself and do it from time to time. Each time their face is painted, ask them if they would like to have it for the rest of their life. Ignore the answer. You are only planting the question in their head.