What Nusach did Rav Kook daven?
ב"ה Shalom Rav Kook zt"l davened nusach Ashkenaz and that is the nusach of the siddur "Olat Re'eiya" which contains Rav Kook"s commentaries on the siddur. In the notes written by his son Rav Tzvi Yehuda Kook zt"l,(Vol. II, pg. 490) Rav Tzvi Yehuda writes how Rav Kook his father , who understood the Kabbalistic underpinnings of the Kedusha, longed to say "Keter" which is in nusach Sfard. All the best.