Actually, the "Longstreet is slow" canard was part of the Lost Cause nonsense made up by Jubal Early and his cohorts years after the war. I have not come across anything written during the war that accuses Longstreet of being "slow".
In a 1998 article Gary Gallagher addressed many of the erroneous claims regarding Longstreet. He rejected the Lost Cause claims that Longstreet was a slow marcher, pointing out the 1875 statements of George Clay Eggleston that Lee himself said, "...that Jackson was by no means so rapid a marcher as Longstreet, and that he [Jackson] had an unfortunate habit of never being on time".
He also quotes William P. Snow's 1867 work that describes Longstreet as "bold, daring, dashing and a rapid marcher."
[1] Gallagher goes on to examine the charge that Longstreet was slow in reaching the battlefield at Second Manassas, another Lost Cause claim, concluding that; "By any reasonable standard, it was an excellent march that compared favorably with what Jackson's troops accomplished in covering the same ground."
[2]
[1] Gallagher,
Lee and His Generals in War and Memory, 144.
[2] Ibid., 153.