So far this season, The Thinker’s advantage has been that he can out-think everyone. He knows every variable, every possibility, and every probability. Because of that, he can predict people’s behavior and manipulate them. His plans aren’t perfect—Team Flash finds him sooner than he expected—but he can account for changes and adjust as necessary because he knows everything that’s in play. The Thinker knows everything that could happen but he doesn’t know what will happen for sure.
Barry has a way of knowing what will happen (no time traveling required), and that’s how he can beat The Thinker.
Spoilers for 4×09 “Don’t Run”
When Barry was in the Speed Force at the beginning of season 4, he saw his life pass over and over, past and future, out of order. He came out of the Speed Force confused and seemingly spouting nonsense. Except…it wasn’t nonsense. Barry was quoting himself out of context. He was talking about things that have already happened (“Every hour, every minute”) and things that haven’t happened yet (“We’re gonna need more diapers”).
Barry reverted back to his normal self at the end of the season premiere and couldn’t remember what he was saying, but what if that knowledge is still in his mind? What if he just needs a way to access it?
If Barry can figure out how to remember what he experienced in the Speed Force, then he can figure out how to beat The Thinker. Or rather, how he (already?) beat The Thinker in the future. Barry can see what actions he took. But The Thinker can determine only possible outcomes.
Team Flash hasn’t figured out how to beat The Thinker yet, but now they have a key.
The Thinker framed Barry for murder, and soon, Barry is going to be on trial. He’s going to say something that sounds familiar, but before, seemed like nonsense right after he came out of the Speed Force: “Your honor, I’m innocent. I didn’t do this. I didn’t kill anyone.”
After Team Flash to realizes they’ve heard Barry say that before, they’ll realize that maybe Barry knows what happens in the future. And then they can help Barry access that knowledge.