Flowing Haki is literally letting the Haki appear in your arm/weapon. Many marines randoms could do it in DR, and no, they dont have Barrier Haki.
Barrier Haki is letting the Haki exit your body (swordsmen and any weapon user that can use Haki on their weapon are in contact with their weapon). And when Rayleigh explained Hakis, Luffy asociated Adv Haki with Boa sisters and Hardening with Margaret's coated arrow.
So coating your weapons is not Barrier Haki, it's basic hardening. Zoro does not know Barrier Haki. Only Enma could make him throw Haki away.
Barrier Haki is letting the Haki exit your body (swordsmen and any weapon user that can use Haki on their weapon are in contact with their weapon). And when Rayleigh explained Hakis, Luffy asociated Adv Haki with Boa sisters and Hardening with Margaret's coated arrow.
So coating your weapons is not Barrier Haki, it's basic hardening. Zoro does not know Barrier Haki. Only Enma could make him throw Haki away.