Question: Looking for movie featuring Dragons vs. Navy (or Army, but the trailer featured battleship trying to shoot the dragons down).

Trailer also showed a dogfight between helicopters and dragons, capping (on the trailer) with a dragon setting a Blackhawk's blades on fire.

Answer: 
I saw that trailer too and then could not find it again , but stumbled across it today ,it is called Crimson Skies 

Only other info i could find on this is that it was originaly called Dragon seige but your guess is as good as mine as to wether its movie or game
MainStay Productions released a trailer on YouTube last year, about a movie project they are working on with BluFire Studios, ostensibly called Crimson Skies.
The premise is that a volcanic island erupts, releasing thousands of dragons from millenia-long slumber, that attack a small fleet of Navy vessels.

I checked on both MainStay and BluFire's websites, neither of which make any mention of the project, which makes me think that the trailer may simply be a "pitch demo" to try and find a studio willing to underwrite it. There is no other mention of the movie, other than the video, that I can find. 

Of course, this may also be just another elaborate YouTube hoax.