Militarily, False Flags are intended to distract and protect (draw away).
I am hard pressed to think of an example of an FF that influences the enemies forces.
https://en.m.wikipedia.org/wiki/Gleiwitz_incident
The Gleiwitz incident was a covert Nazi German attack on the German radio station Sender Gleiwitz on the night of 31 August 1939 (today Gliwice, Poland). The attack is widely regarded as a false flag operation, staged with some two dozen similar German incidents on the eve of the invasion of Poland leading up to World War II in Europe. The attackers had been posed as Polish nationals. Adolf Hitler invaded Poland the next morning after a lengthy period of preparations. During his declaration of war, Hitler did not mention the Gleiwitz incident but grouped all provocations staged by the SS as an alleged Polish assault on Germany. The Gleiwitz incident is the best-known action of Operation Himmler, a series of special operations undertaken by the Schutzstaffel (SS) to serve Nazi German propaganda at the outbreak of war. The operation was intended to create the appearance of Polish aggression against Germany to justify the invasion of Poland. Evidence for the Gleiwitz attack by the SS was provided by the German SS officer, Alfred Naujocks in 1945.
So technically maybe more like staging an incident in order to raise the bloody shirt?
When the seals went ashore in front CNN during desert storm it influenced the Iraqi Forces.
If that is considered a false flag
“I am hard pressed to think of an example of an FF that influences the enemies forces.”
Is drawing them away not influencing them?
At its core, false flags are things done by someone that are blamed on others, usually to advance the desires of the former.