In the introduction to his work, Kohen provides a purported lineage going back over a dozen generations of kohanim born at Djerba.
Among his claimed patrilineal ancestors are Rabbi Shaul HaKohen [he] (d. 1848), himself an author of multiple works on Hebrew grammar.
Citing a similar lineage table from Heritage of Yehoyada HaKohen (נוריש יהוידע הכהן), Kohen claims to trace the family back to Yitzchak HaKohen the Elder, who had emigrated from Israel to Djerba at the Second Temple Destruction.
[1] The work purports to present the "authentic" pronunciation of the 22 Hebrew letters based on Geonic literature and the work of Hebrew grammarians such as Rav Saadya Gaon, Rabbi Yitzhak ben Shlomo Yisraeli and the Radak.
The table was published (with minor variations from what is listed below) on page 150 of Sfath Emeth: