If you want a good picture of a Chaos uprising in 40K, ISIS/ISIL/Islamic State seems like a pretty good model.
- Take advantage of existing unrest, turning it to own ends.
- Absorb turncoats into your ranks and make use of captured equipment.
- Destroy rival religious sites and iconography.
- Atrocity as a goal itself as much as a tool or byproduct.
A lot is similar to other revolutionary movements of course. You could easily put a Chaotic spin on numerous past events and movements - the French Revolution, the Khmer Rouge, various religious conflicts, etc. and use them as an inspiration for a Lost and the Damned force. If you're looking for inspiration from GW sources, check out my Lost and the Damned Bibliography.
“Power is not a means; it is an end. One does not establish a dictatorship in order to safeguard a revolution; one makes the revolution in order to establish the dictatorship. The object of persecution is persecution. The object of torture is torture. The object of power is power.” - George Orwell (1984)