Despite my thorough research into the databases and the references given, I haven’t found any further editions of L’anfiteatro Flavio by Carlo Fontana published before 1800. Perhaps the fact that even the first edition was published posthumously in 1725 had something to do with it.
The earliest reedition I could find was published in 2002. It is an anastatic edition of the original manuscript, edited by Hellmut Hager:
Fontana, Carlo / Hager, Hellmut (2002). L’anfiteatro Flavio, anastatic edition of the manuscript in the Museum of Rome, Rome