Thats an excellent observation!!! and exactly the kind of thinking that often presents great clues in the study of weapons development. Very impressive, and actually I had never noticed that particular similarity.
It is well known that many ethnographic weapons bear striking similarity to ancient weapons found typically in iconographic sources. Atavistic forms have often been believed to have been the influence in many later developed weapons in various cultures. Clearly the Greek kopis, the machaira and the Egyptian khopesh are prime examples.
The flyssa is a relative newcomer among many of the swords of North Africa, and its origins are somewhat obscure and obviously widely debated. I am inclined to believe that it likely is derived from early forms of yataghan with somewhat the same deep bellied blade form, as seen in the c.1510 example shown in "The Age of Suleyman the Magnificent" (1990, p.64, #50). There is clearly a considerable gap in time from the period of this weapon to the first known appearance of the flyssa c.1827, but again the expanses of time between the kopis' and machaira that likely were the inspiration for the Ottoman weapon are obviously as broad, and demonstrate the atavistic perspective descibed.
In using the search feature here, it will be seen that there have been many discussions on the flyssa, especially on how it may have been used in combat. Its use in combat seems supported as I have discovered one among the holdings of a Foreign Legion museum in France which was taken in battle in 1857. Much as the Black Sea 'cousin'
of these interesting swords, the flyssa left the working weapon group in a short period, probably about the early part of the 20th c.
Best regards,
Jim