Green’s Dictionary of Slang

(US) an important person.

1909		in H. Sampson Ghost Walks (1988) 487: Big Smoak, Big Noise.
1936		E. Barnard Rider of the Cherokee Strip 133: He had charge of all the roundups [...] and was considered a big smoke [DA].
1977		in K. Gilbert Living Black 165: I knew all the big smoke but still I wanted to go through the law.