Batman's team was established after he resigned from the Justice League following sanctions put on the League by Lex Luthor in his new role as Secretary General of the United Nations. In this coordinated walkout, he tooks a number of allies with him. Batman set out to form a covert team who were able to achieve things in service of the greater good that the League would now be unable to do.
Black Lightning turns down an offer to join Batman's group, referring to it as "Batman Incorporated." Batman Incorporated is an organization funded by Wayne Enterprises, made up of the Batman Family and the Batmen of All Nations (and their successors). It was formed to stop crime and make Batman to a global franchise.