[W. Deranged]

With probably 13 or 14 outs here (I think you're As are like 1-2 outs usually) I think you should bet. Betting does a bunch of good things:

1. You have an equity edge if you get called in four places and probably one even if you are just called in three places. With only two callers or a raise and a call, you are just a hair below neutral. The only really bad scenario involves getting check-raised and the hand ending up heads-up.

2. Your hand has a tiny bit of showdown value and betting now might allow you to cash that in the tiny percent of the time it applies (this is a small consideration).

3. Betting may actually mean you get more action on your flush as it makes your hand harder to read.

4. Betting might fold out Ks and clean up your 8 outs some of the time.

And so on.

Basically the idea is that a bet is almost never going to be "bad" (namely more than very slightly negative EV), and often can be quite good. So it seems to me pretty clearly higher EV than checking.