I could see Doug Liman doing this well, in terms of getting a Flash that fits into the current DCCU. Things would be "serious" as Snyder wants, but still provide a good amount of fun.
That being said, I wouldn't want Doug Liman, or any director, unless they themselves WANTED to direct the film as their own passion.
But yeah, style wise, I can see Liman fitting into what DC wants. It'd probably lose much of the comic essence of the Flash, but... it'd fit. That being said, I don't see the Flash or superheroes being his personal choice, so in that aspect it wouldn't work out, since he'd probably turn it into some... spy movie...