In which episode of the Arrow does the Black Canary get her "cry"? Or was it a Flash episode? I seemed to have missed this one.
The current Black Canary no longer has a "Canary Cry" device; she's a metahuman who can make that sound naturally.
The device that Laurel used, called the Canary Cry, was given to her on an episode of The Flash called "Who is Harrison Wells?" (S01E19). This is a minor crossover, where Joe and Cisco go to Starling City to dig up information on Harrison Wells, whom they are beginning to suspect is hiding something. Cisco takes one of Sara Lance's "sonic grenades" and converts it into the Canary Cry for Laurel, and gives it to her at the end of that episode.
The "sonic grenades" are devices Sara was shown using from the very first episode she appeared in. I don't think we are told where she got them, but they are the kind of slightly-exotic weapon you might expect the League of Assassins to have. Sara had multiples of these, and typically threw them on the ground like a grenade, as opposed to using it via her own voice.