Say on; say what you have to say. The allusion to firing a gun; as, You are primed up to the muzzle with something you want to say; fire away and discharge your thoughts.
“`Foster, I have something I want you and Miss Caryll to understand.' `Fire away!' exclaimed Foster.” —Watson: The Web of a Spider, chap. xv.
Fire away, Flanagan. A taunt to a boaster. A man threatening you, says he will do this, that, and the other; you reply, “Fire away, Flanagan.” Cromwell marched against a castle defended by Flanagan, who threatened to open his cannon on the Parliamentarians unless they withdrew. Cromwell wrote on the corner of the missive sent to him, “Fire away, Flanagan,” and the doughty champion took to his heels immediately.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894