this is common sadly. its probably down to the weather being so changeable. Though i have a sneaky feeling the plant 'decides' its too small to support too many flowers and aborts the other buds.

Give it a good feed about now with a general purpose liquid, like Maxicrop or Baby Bio or whatever and it should be set up nicely for next season.

One of my Peonies is in its 2nd year and I have had no flowers.I dont really expect any in the first 2-3 years but the wait is well worth it,