The Vilna Gaon, who Ha Rav Meir Kahane (zt"l) based almost all his opinions on, stated that any sworn enemy of the Jews in any generation is Amalek.
Your statement is part correct and part mistaken, I think.
The Vilna Gaon,
who Ha Rav Meir Kahane (zt"l) based almost all his opinions on,
While Rav Kahane certainly drew from the incredible wisdom of the Vilna Gaon, it is not true (to my understanding) that he "based almost all his opinions" on the Gaon. I'm not sure it can be said that Rabbi Kahane based almost all his opinions on any single Torah authority. His parsha talks and articles seemed rather ecclectic to me, which I think is a huge strength.
That being said
The Vilna Gaon,
stated that any sworn enemy of the Jews in any generation is Amalek.
Yes. And Chaim has repeated this opinion of the Vilna Gaon several times on the ask JTF program. I think there was another authority who also held this opinion. The Gaon said that any nation that makes war against the Jewish people takes on the identity of Amalek. Yup, no escaping the facts.