He studied at Mannheim with Ignaz Holzbauer and Georg Joseph Vogler before going to the University of Würzburg. He then became private secretary and tutor to the Regierungs-präsident at Regensburg in 1786, before going on to be cabinet secretary to Georg I, Duke of Saxe-Meiningen. 1792 he married at Themar Johanna Christiane Louise von Schulthes (1771-1856, daughter of Johann Adolf von Schultes). They had several children.
His son W. Th. Fleischmann (1794–1886), had a son F.C.W. Alexander J. Fleischmann (1826–1891). Alexander J. Fleischmann translated the book Looking Backward by Edward Bellamy into German. („Ein Rückblick aus dem Jahre 2000 auf das Jahr 1887“, Wiegand, Leipzig 1890). During one year seven editions were printed.
B.A. Johanna Müller (artist name: Müller-Koburg, 1860–1947), daughter of Alexander Fleischmann, was a writer, painter and translator; she painted landscapes (Baltic Sea, Berlin, Coburg and the artist colony Ahrenshoop).
- Rönnau, Klaus (1992), 'Fleischmann, Friedrich' in The New Grove Dictionary of Opera, ed. Stanley Sadie (London) ISBN 0-333-73432-7
- E. Goretzki and D. Krickenberg (July 1988) 'Das Wiegenlied "von Mozart"', in Mitteilungen der Internationalen Stiftung Mozarteum, Salzburg (S.114 ff)
- Marktheidenfeld honors its composers (German)