There are strong indicators that "Jihad" was used not in a sense of armed struggle there, but more akin to a social revolution; "thinking machines" were declared a problem not because they were a physical threat a la Saberhagen's Berserkers, but because their influence on society was deemed overly negative.
Given that, a book that would cover the Jihad would probably be another philosophical treatise in the vein of God-Emperor of Dune.
The Dune Encyclopedia had a couple of articles on the Butlerian Jihad. All of the material was invented for that work -- Frank Herbert's novels only had the barest shred of explanation of what it was -- but their theory was fairly reasonable, and were consistent with the spirit of his writing. (In summary, a hospital's "self-programming computer" terminated a Bene Gesserit woman's pregnancy; her protests ignited existing tensions against computers and high technology.)
Given that, a book that would cover the Jihad would probably be another philosophical treatise in the vein of God-Emperor of Dune.