Jack Goldsmith and Oona Hathaway explain at length why an attack on Syria would be illegal:

Bottom line: If you support the coming air strike in Syria, you are supporting a rationale that allows the president to use air power unilaterally basically whenever he sees fit.

2. The coming air strike will violate international law. The United Nations Charter prohibits “the threat or use of force against the territorial integrity or political independence of any state.” This most important of international laws has three exceptions, none of which are implicated here: First, Syria has not consented to the strikes; second, the U.N. Security Council has not authorized the strikes.; and third, the United States is not acting in self-defense.

It is worth noting that these legal interpretations aren’t being seriously disputed by anyone. There is a fairly broad consensus that there is no legal justification for the attack that is probably starting in the next few days. No one honestly thinks the president has the authority to order attacks against states that haven’t attacked us or our allies, and no one is claiming that an attack wouldn’t violate international law. The illegality of attacking Syria is obvious and undeniable, but Congressional leaders simply don’t care. Congress’ abdication in matters of war is not new, but it is particularly dangerous at the moment when there is a real possibility that a reckless president will order attacks on the forces of as many as three other governments. Trump’s domestic critics that have pleaded with him to take a harder line with Russia are about to get their wish granted in the worst possible way.

Hawkish interventionists like to talk about how the U.S. upholds the “international order,” but a U.S.-led attack on Syria would be one of the most egregious violations of the so-called international order in at least the last thirty years. It would be a direct assault on one of the bedrock principles of the post-WWII international system, and it would constitute a flagrant breach of the U.N. Charter. The U.S. would be demonstrating to the world once again that it disregards its international obligations whenever it pleases and can’t be trusted to honor its commitments.