What kind of false flag operations would be possible in a universe where advanced AI exists along with fairly reliable FTL travel and multiple alien species and human factions all vying to be top dog?
The scenario has multiple alien and human factions that are all vying to be top dog. This suggests a given alien or human faction might disguise its AI or FTL technology to resemble that belonging to another faction. Obviously this could be used in covert operations against other factions.
Interesting a human faction A could disguise a FTL vessel as a vessel belonging to alien faction X. Its AI would be disguised as an alien faction X AI. Then human faction A could launch an covert operation against human faction B in hope that they will retaliate against alien faction X.
This could be further complicated if human faction A constructed an AI that resembled an alien faction Y AI and then disguised it as an alien faction X AI. The attack could be aimed at human faction B. Because this is a multiple layered false flag operation, human faction B could retaliate against either alien faction X or Y.
The nature of the FTL travel and the types of AI in your fictional universe will be a major determinant of the kinds of false flag operations that could be undertaken. The most likely form they take is due to the fact that both FTL vessels and AI are artificial constructs that any faction, either alien or human, will be able to duplicate those of other factions.
Advanced AI might actually help a false flag operation. So Faction X intends to commit a crime or deed and frame Faction Y. An Advanced AI can ensure that no trace of Faction X exists, and the evidence for Faction Y being the culprit is flawless.
That is the purpose of the AI, to make accurate predictions about what will happen and how it will be perceived; that is the (in my view) the definition of a good AI.
On the other side, this can mean an AI investigating the case will also find no trace of Faction X, and several traces of Faction Y; so the false flag succeeds: The AI owned by Faction X can ensure that to either people or other AI, the evidence is indistinguishable from an actual Faction Y deed.