US-lead military intervention in Syria was always going to be technically illegal so long as it did not get the approval of the Security Council. But with the British dropping out of the fight, the Arab League cautioning against military strikes, and other would-be allies going wobbly the impending US strike would lack legitimacy, too.
“Legitimacy” is a key component of just war theory. The idea is that before declaring war, you have to have proper authority to do so. In a democracy, this is used to be fairly straightforward: elected leaders use constitutional principals to invoke their authority to go to war. But ever since the end of World War Two, as modern structures of international law and modern alliances have taken hold, authority has also been derived from the Security Council; or failing that, a broad coalition of democracies working in concert. The Kosovo war was technically illegal, but you can make a compelling argument that it was still legitimate for the fact that a broad European alliance (NATO) intervened to take care of a problem on their borders.
The impending US intervention in Syria is shaping up to be both illegal and lacking legitimacy. The notion that the USA can intervene to enforce prohibitions against chemical weapons use is compelling to the extent that other countries — a particularly those in the region — are broadly supportive of this effort. But lacking Security Council approval, and lacking buy in from some of the key international stakeholders, like the Arab League, it is hard to make a compelling argument that the USA has the authority to enforce this norm.
A president’s decision to wage essentially unilateral war to enforce an international norm does not a legitimate intervention make. It also sets a very dangerous precedent.