Question
can you grow peonies from the pods of the flower after it has bloomed

Answer
Hi Ron,
Thanx for your question.  I have had no luck finding seeds on the spent pods of my peonies however, I do know that some peonies will set seed.  The seeds I have seen are black and pea-shaped.  Mostly, these come from native Chinese varieties.  If you are lucky to get seeds, they will need to be cold treated for 60-90 days in order to break dormancy.  Place the seeds in a moist paper towel and seal inside a plastic baggie and store in the fridge.  
The best way to grow more peonies is to dig up the rhizomes and separate the growing points.  You'll get results quicker.  Seed-grown peonies could take 5 years or more for bloom.  Rhizomes will require 1-2 years (sometimes three if the peony gets really ticked off at you for disturbing it.  They do not like their roots disturbed.).  I hope this helps.
Tom