Yes this is very good for gaming and if you shelling out for SLI on the 760s you might as well go for 8gb of RAM because IMO your gonna start needing it in the future and Yes everything is compatible pcpartpicker would have given you a message in red if some components weren't. My pc has 8gb RAM and goes near 95% RAM usage when playing BF4 when theres tons of action along with maybe a window or two of chrome open
The CPU's good. I'm not sure about the cooler, its compatible, but I've heard many great things about the CM Hyper 212 Evo for around the same price. The motherboards good and is compatible with your 2x gtx 760's, but you definitely want 8gb of ram. You don't need more than 8gb unless you're doing quite a bit of video editing, rendering etc, but you want atleast 8gb for gaming and general usage. G.Skill itself is a decent brand, but I would also recommend Kingston or Corsair ram as well if you had no particular desire to go with g.skill ram.
Rather than the Mushkin Chronos, I would get a Samsung Evo 120gb. I've had a great experience with that drive personally and performs beautifully and for a great price too. It would just be a little more "solid" IMO. The HDD is a good choice, I would personally go for the 1tb edition but that depends on your own storage needs. Everyone is different. If you want better performance though, I would go for the black edition of the drive.
The 750w corsair is a good choice, I would go with an 850w for the extra headroom for overclocking, extra fans, hdds etc though. Although you will likely be fine with the 750w anyway.
The case is a matter of preference. I would get a slightly higher quality case if I were you, but if you want to stick in that price range the Corsair 230t is a great "budget" choice. From what I've seen it packs a tonne of features and really is a great deal for the price.
The rest of the build looks good. If you are on a tight budget, ditch one of the 760's and get a 770. That will give you a bit of headroom money wise.. A single 760 is still prety strong for 1080p though and it will play Battlefield smoothly at high-ultra settings.