Viorel's question may take you there. But probably you have an idea of the JSON should look like. And no matter how you want the JSON to look, you probably can do it from T-SQL by spawning out to BCP. But just because you can, does not mean that you should. This task is probably a lot better done with a client-side program that reads the rows and then writes the JSON to file. No matter you use SSIS, Python. .NET, Java or whatever, it is likely to have better capabilities to control the JSON than T-SQL have.
And note that BCP is just another client-side program really. It is not the best to create JSON files though.