sumac, cloth woven from tree fibres
栲 centers on a specific tree, the sumac, and the cloth woven from its fibers. The two meanings are directly connected: the tree provides the material for the cloth.
栲 combines 木 (tree) with 考, which likely contributes the sound. The character refers to the sumac tree and its fibrous cloth.
A tree 木 that you can think about 考: the sumac tree, whose fibers are woven into cloth.
For コウ, imagine a coat woven from sumac cloth: coat -> コウ, and the tree provides the fibers.