The composers and musicians active in the Marktheidenfeld area, Fathers Franz Xaver Bitthäuser and Peter Dornbusch of the Augustinian Canons' Monastery in Triefenstein and Peregrin Pögl of the Benedictine Abbey in Neustadt were his first teachers as well as his father. From the local school he transferred at the age of eleven to the grammar school in Mannheim where he was taught by Ignaz Holzbauer and Abbé Vogler. From 1782 he studied at the University of Würzburg where he received his doctorate in 1783 and went on to study law.
In addition to his work as cabinet secretary, Friedrich Fleischmann was active as a musician in the Meiningen court orchestra and also as a composer and music theorist.
Most of his compositions were published by the music publisher André in Offenbach.
In 1796 he wrote the Singspiel ''Die Geisterinsel''. Researchers now consider it very likely that the lullaby "Schlafe, mein Prinzchen, schlaf ein" (Sleep, my little prince, Fall asleep) which was previously attributed to Wolfgang Amadeus Mozart (KV 350) or to the Berlin physician Bernhard Flies was actually written by Fleischmann (research by E. Goretzki).