In 1946 he was a founding member of Talich's Czech Chamber Orchestra, between 1953–1976 the viol da gambist of Pro Arte Antiqua (one of the oldest European ensembles focused on medieval and Renaissance music) and between 1954–1997 a member of the ensemble Ars Rediviva, whose performances and recordings played an important role in the revival of the Baroque music in Czechoslovakia.
[citation needed] With these ensembles he made a large number of recordings (with Supraphon, Panton, Columbia, DGG, Ariola, and Nippon), which received several awards both in Czechoslovakia and abroad (e.g. Grand Prix du Disque).
In 2001 his book "Z Herálce do Šangrilá a zase nazpátek" (“From Heralec to Shangrila and Back Again”) was published - reminiscences about the Prague music scene between the 1940s and the 1990s as well as about Sláma's musical colleagues, conductors (Talich, Barbirolli, Cluytens, Karajan, Kleiber, Klemperer, Kletzki, Kubelík, Maazel, Mackerras, Markevitch, Matačić, Mravinsky, Münch, Pedrotti, Rozhdestvensky, Sawallisch, Stokowski, etc.)
and other personalities whom he had met (e.g. Adorján, André, Fournier, Honegger, Mainardi, Menuhin, Milhaud, Navarra, Nureyev, Oistrakh, Rampal, Richter, Szeryng, Sudek, Tortelier).
František Sláma archive collection donated to his native village Herálec consists of more than 5,000 negatives and photos, over 150 hours of authentic recordings and documents about Czech Philharmonic Orchestra, Václav Talich, Milan Muclinger, Ars Rediviva, etc.