I actually looked at the firebombing of Tokyo rather than the atomic bombings (the a-bombings have been looked at a lot more frequently, and are a lot more fraught because they ushered in the nuclear age, but I digress). Slightly different context but the issues of legality are largely the same: in both instances there was a large-scale targeting of civilian centers, without any pretext of even trying to focus on targets of military value.

I concluded that it did violate military law, which didn't forbid attacks against areas where civilians might be present but, at an absolute minimum, required that the attacks focus on identifiable military targets. These attacks failed that test because they simply tried to burn out the entire city: cultural, civilian and military centers alike.

However I also concluded that it would not have served justice to prosecute the generals who ordered these attacks (unlike the atom bombings, due to idiosyncrasies in the chain of command the firebombing of Tokyo, which killed more people than either atomic bombing, was largely the decision of a relatively junior field commander, Curtis Lemay). This is because, by this point in the war every major power, axis and allies, had abandoned any pretext of following Hague Convention rules on protecting civilian populations in war zones. No country was honoring the legally required practices to protect civilians, nor had they been for several years. In this environment, it is difficult to argue that a commander following what had become the de facto policy of all major combatants could be singled out for war crimes. Lack of clean hands is largely the reason the Allies never prosecuted any Axis leaders for attacks against Allied civilian populations. In the case of the a-bomb it's a slightly different analysis since Truman, rather than a 2-star general, made the call, but probably the same conclusion.