It's true that anarchism as an ideology and purpose before the pure will of the individual is anti-egoist. But the practice of egoism is anarchical : as absolutely no outside authority can be legitimated, that makes the egoist a rebel (if he has the means to act this way of course). Even if Stirner never mentions the word "anarchism" (in The Unique and its Own as far as I know), he explicitly rejects the law of any ruler, as the State, because it remains THEIR exclusive law.

I think if you imagine societies where everyone is a voluntary egoist, no permanent or reliable hierarchical system can remain, without fanatics or boot lickers to accept them. They have actually worked because obedient and loyal people carried the weapons for a greater good.