The brilliant keepers of the IMSLP tracked down the origins of the well-known Fiocco Allegro. It is number 10 in a set of Pieces de Clavecin he published in 1730.
There are eight lovely character pieces written in a very French manner, but after just a quick look at number nine, the piece that precedes the famous Allegro (made famous by its violin transcriptions), it is clear (to me, at least) that Fiocco was imagining an Italian violin concerto (to be played on the harpsichord).
The last movement is so violinistic that I couldn't resist making a full-fledged transcription to use for next year's Summer Strings.
The deed is done, and the music is available through this link in the IMSLP.