This is the 8456th most frequent Japanese word.
成り
"成り" (Nari) means "becoming" or "resulting in" and can imply a state, condition, or transformation.
成り行き refers to the course of events or natural progression.
これが成り行きの流れだ。
This is the flow of events.
成り is used here metaphorically to denote establishment or distinction in a certain role.
彼は棋士として成りを画した。
He distinguished himself as a shogi player.
成り立つ combines '成り' with '立つ', meaning become established or hold together.