I've been meaning to check this place out for a while. It not too far from the Trionfale farmers market in Prati.
On the first floor are plants/trees and on the second floor are cut flowers.
It's open to the public on Tuesdays after 10:00 a.m. Many of the cut flowers are gone by then, but the prices are incredible cheap.
Mercato dei Fiori
On the corner of Via Trionfale and Via Paolo Sarpi
Peonies are among my favorite flowers. They are not cheap. However, this bunch cost only five euros and opened up nicely.