What does a peoney flower tattoo symbolize?

Peony represents healing, to heal, or the healing process.

In Europe the Peony is referred to as 'a rose without thorns' and has been a way to refer to the Virgin Mary. It is associated with dignity and honor.

In Japanese tattooing it symbolises wealth, good fortune and prosperity, although it can also be associated with gambling, daring and a devil-may-care attitude
In Japanese and Chinese Culture the Peony Symbolizes Wealth, Good Fortune, and Prosperity. Yes it is sometimes used as a filler for Asian Derived tattoos. But the Peony itself means all of that.