Ewald's biography of Charles, published in 1904, states that both Charles and his brother Henry were musicians and as young men in Rome gave weekly concerts for the Rome elite and Charles in particular as a cellist was considered a finished musician. It then gives an extract from the diary of Charles Desbrosses, first President of the Parliament of Dijon who says the he entered a room when the brothers had already commenced Corelli's "Notte di natale". When it was over Desbrosses seemingly exclaimed that he was so sorry he'd missed the beginning so Charles insisted they play the piece again prior to starting another piece!

Not that it proves anything other than the Prince was a musician so it is possible he owned and even played the flute.