Are you considering growing from seed or buying in plants Goldilocks? If the former it will certainly take them several years from seed sowing to a established plant able to flower but if you buy in well grown plant they should flower that year. I am also assuming you are asking about deciduous peonies not tree peonies. The RHS site has some excellent advise on growing copy and paste the link below into your browser:

https://www.rhs.org.uk/advice/profile?pid=671

thanks. I would rather have a well grown plant.

Well now is the time to buy and plant so off you go to your local nursery :)

Hi, when you plant them, remember to plant with the tops of the tubers just visible when the soil has settled, this will help towards flowering next year, the main reason for Paeonies failing to flower after being transplanted is being planted too deep, and remember these are very long lived plants, so make sure they're in the right place, as they resent root disturbance, [ I have paeonies in my garden, which were here when my parents and I moved here 57 years ago, and still going strong,] Derek.