Yeah, I'm kinda with Forkfoot. I'd even go as far as to say that the idea of narrative and storytelling is getting kinda old. It's like eating Italian food everyday of your life; there's some variety, and it's capable of being good, even great, but after a while it just isn't satisfying. Messing with chronology is one way to try and revive the format, but even that is fairly commonplace and ultimately pretty superficial. One of the most interesting novels I've read recently, Autofiction by Hitomi Kanehara is in three parts, and each part is basically just a sketch of this character at the ages of 22, 18, 16, and 15, and Kanehara is never really interested in telling a story or captivating the reader with narrative, she's only interested in presenting this character and exploring the way understanding can be distorted and kinda reflexively analysing the fiction process. But anyway, I'm getting off-track. Basically, I think chronology is one good tool, but it's a fairly superficial one unless you use a non-linear order to reflect in the text on the effects of that order. If the story could be told in the same way going beginning to end, then there's no point changing the chronology arbitrarily.
That sounds like the sort of novel I'd be into. Yeah, I guess that's what it is for me; narrative as it stands feels dried up and long in the tooth. What catches my attention now are moments; an instant the artist points to which makes me go "Ah!" without a story really being needed. The only non-comedy films I've enjoyed recently have been documentaries, a very few "art films", and Avatar, because I can watch it without paying attention to the story and still be amazed. Anything else has a hard time competing with how amazing the walk to the theater was. Tarantino seems to do it pretty arbitrarily a lot of times. Even in situations like that, though, it still draws my attention more than linear-chronology narrative. Maybe it's because life as it's actually experienced isn't chronological; in our minds we flash back and forth between past, present, and dream sequences nonstop. When it jumps around like that, to me it actually feels smoother; flows better.
I think for it to work the reader will have to be conscious of the conventional chronology because that is how we perceive and interpret whatever passes for the Real World. Messing with that chronology is a tool that's available, but mess with it to the point where the reader has trouble following? Well, maybe the first time somebody comes across it they'll think "hey, neat!" but the next time their reaction will likely be "This is old news; I've seen it before." Seriously messing with chronology is rarely done for much the same reason as there's only one Finnegan's Wake. Even if it's done brilliantly, most of the value lies in the novelty, so as soon as other people start doing it the reason for doing it is lost. As somebody else said, it becomes a gimmick.
