Asura is an extension of Zoro’s usage of the concept of flow. I think Zoro already had a good mastery of the concept since the first time he used it.
Before Zoro uses Asura, he always has to establish a certain domain around him. That is the area of effect created by Conqueror’s Haki, where Asura operates inside, represented by a black background.
Next Zoro starts to create additional arms and heads (the limbs he holds his swords with). It’s interactable (blocks and cuts) not just a visual illusion.
Here is where the concept of flow comes to play: We know that the concept means gathering the unnecessary Haki that surrounds the body and make it flow through a certain body part or weapon which makes the Haki take the shape of an invisible armor.
The assumption that this theory stands on is that with enough mastery of the concept the user can extend or manipulate the shape of that armor to his liking.
It’s very close concept to the advanced Nen technique in Hunter X Hunter, specifically transmutation shape shifting like when Biscuit forms invisible numbers through manipulating the shape of her aura.
So Zoro most likely surrounds his body with the flow and then he expands certain areas and manipulate its shape ti make it look like he has additional arms and heads. But then one would ask the question why is Asura visible when the flow is not?
This is where Conqueror’s Haki comes into play. When it’s fused with Armament Haki it makes the flow visible. And the best proof of that is when Luffy hit Kaido with Red Rock. Kid was wondering about the Haki that Luffy used when he shouldn’t be able to see it in the first place.
Another one (this might be a stretch) is when Zoro was getting ready to do Tatsumaki and Kaido notices something strange about his Haki, where he should only see hardening.
So this process is about 3 stages (sorry for the bad drawings):
1- Surrounding the body with the Haki flow.
2- Manipulating the shape of that flow.
3- Adding Conqueror’s haki to create the visible illusion.
*Theory by draganax