It seems we can discount Jackson a the originator of the term. The earliest record I've found comes from a report on troops at Fortress Monroe in the New York Commercial Advertiser, of 7 June 1861. An officer of the Zouaves is quoted as saying: "The Secessionists aver that they are not afraid of the Troy, Albany, Colonel Allen's or the Vermont Regiment, but they would rather keep clear of the 'red legged devils,' as they call Duryea's Zouaves."
Just how said officer knew what "the Secessionists aver" in this regard is unclear. It sounds very much like what the Zouaves themselves wanted to be called.
Did Jackson use it? Seems doubtful.
jno