"He took a good part of his corps to the Army of the Tennessee in September and played a leading role in achieving that army's only tactical victory at Chickamauga, an offensive triumph. But Longstreet argued viciously with its commander, Gen. Braxton Bragg, about the strategic follow up. ....."
I have never seen any account that Longstreet "argued" with General Bragg. He certainly disagreed with some of his decisions, as he claims in his memoirs, and attempted to share his opinions, etc. with his seniors.
Viciously, 1828 definition:
VI'CIOUSLY, adverb
1. Corruptly; in a manner contrary to rectitude, moral principles, propriety or purity.
2. Faultily; not correctly.
So Hess is stating that Longstreet's arguments against Bragg's strategy after Chickamauga were faulty and incorrect.