It's a first name that goes back to the Middle Ages. It's the name of the love interest of the Italian 14th century writer Giovanni Boccaccio (like Beatrice for Dante and Laura for Petrarch). He wrote a book entitled: "Elegia di Madonna Fiammetta". Fiammetta is also one of the narrators in the frame story of the Decameron.
This name is just amazing. Not everyone could pull it off, and apparently not many people are brave enough to use it. I certainly encourage it to be used more often! Strong and unusual, with a fantastic meaning and history.