Trump will wag his finger at Assad until he thinks the news cycle is over, and then he'll shut up.
And that will be that as it goes for the story.
If we go to war in Syria, it won't be against Assad. If anything, we'll end up aiding and abetting him while we claim to be fighting ISIS. For him, ISIS makes a better enemy because Islamic extremism sells better to his crowd than war crimes.
He's not going to cross Putin when it comes to Assad, and besides, Assad's a strongman and Trump secretly likes strongmen.
He doesn't actually care about Assad gassing his own people. You know the things Trump cares about, because he tweets about things he cares about. Meryl Streep criticizes him in a Golden Globes speech, and the very next morning he lets out a volley of tweets against her.
He hasn't tweeted a single thing about what happened in Syria since it hit the news. All we got was a terse four sentence statement with two of those sentences blaming President Obama for what happened. And he sent Nikki Haley off to the UN, an organization he doesn't give a shit about and Putin doesn't give a shit about, to do a Kabuki dance of concern about Syria and Russia.
All this will last until he feels the story is sufficiently over with, and never again will we hear about it, unless perhaps Assad decides to gas more of his people.