No, it's going to be Barry.
I'd watch a Jay movie (or a Wally or Bart movie, for that matter) but this is a Justice League origin story and they're going with the most iconic versions of the characters. We're not going to see Arthur Joseph Curry, Jay Garrick, or Simon Baz. It's going to be Arthur (Orin) Curry, Barry Allen, and Hal Jordan.
They've gone through painstaking effort in the last handful of years to re-establish Barry, Orin, and Hal in the comics, animated movies, live action tv, cartoons, and video games. They wouldn't break that trend for arguably the biggest depiction of the characters: live action film.