After the Great Ninja War, Naruto's right arm was replaced by an artificial arm made up of Hashirama Senju's cells. To perform Wood Style, user requires a vast amount of chakra and Naruto can easily manage that.
Wood Style requires water and earth affinity as it's a combination of these, while Naruto has wind affinity.
Using Combined Styles also requires Kekkei Genkai, which Naruto doesn't have.
So unless the author comes up with something in the future (like somehow forming his own chakra into the one he received from Hagoromo or into the chakras he received from the tailed beasts) Naruto is highly unlikely to be able to use Wood Style.
Given that Naruto has access to Six Paths Sage Mode - a power that gives him instantaneous mastery over the five basic Changes in Chaka Nature + that of Yin-Yang Release, is a reincarnation of Indra Otsutsuki - a power that grants him access to his ultimate form, Asura Kurama Mode, as well gained the affinity of the remaining tailed beasts and was thusly able to master Lava, Boil, and Magnet Release, as seen in Sage Art: Super Tailed Beast Rasenshuriken, I see no reason why Naruto - now also in procession of an arm grafted from cells of the First Hokage, Hashirama Senju, who, despite not being a member of the Otsutsuki clan, mastered Wood Release - should (in theory), be able to use Wood Style were he to meditate on the earth- and water-based nature combination Kekki Genkai using the Six Paths' power.
I would like to believe that he can. There are a few evidences that show this. SPOILER ALERT
After gaining Sage of Six Paths powers he was show to be able to use several kekkai genkai including magnet release, and lava release. While fighting white zetsu his Kyubi cloak the defeated zetsus where turned into a cloak with the 9 tails chakra. During the fight with Pain, after Naruto became enraged and released the 4 tailed cloak, we can see naruto raise a large forest of roots from the ground similar to the Deep Forest Emergence used by Hashirama
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