I have similar problems as they are described in previous posts, since then I have installed AMD Sapphire Nitro R9 380 4GB in my comp.
First I had to download and apply four DLLs from SkateZilla (thanks for these files) to enable to start DCS correctly. Now I can start the game and fly SP missions, but only with shadows set as "FLAT ONLY". If some higher level in shadows settings is used, the game freezes and crashes after the mission is loaded. The other graphic settings does not affect stability of the game.
I cannot start multiplayer using MP icon (only black screen with music in the background), but I can switch to multiplayer from the main screen. I can join servers but only some missions work, sometime DCS freezes and crashes.
I didn't have these problems in DCS 1.5 Beta with previous AMD HD 7850 2GB card, except the starting of multiplayer.
I have no problems with DCS 1.2.16.
Win 7 Home Premium 64bit, DirectX 11, Catalyst 15.7.1 installed.