There are a few ways to implement a custom skybox. I'll focus on 2 of them that I have used:

If you play around in other engines, like Unreal/UDK for example you will see that their skyboxes are just a huge dome that exists so far from the playable area of the level that the user will never be able to interact with it.

Another way of implementing a custom skybox is with a 2 camera setup. You import your skybox game object and assign it to a layer of it's own ie [Skybox].

You create a camera with a depth of 0 and tell it to only render the layer skybox.

Then your camera at depth 1 will be your Main Camera, and it renders everything else but your skybox and has a Clear Flag of Depth Only.

Now if you test your level as is you will notice that if your Main Camera moves your skybox is not tracking along with your cam. You will need to attach a script to your skybox cam which copies the rotation of your Main Camera every frame. This will simulate everything being rendered with the same camera.

Hope that helps,

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Is not possible to make a fbx object as a skybox, skybox are textures that are not possible to reach why would you want to have a FBX? probably I dont understand pretty well.

Can you give us more information about that "Blinking, flickering stuff?"

maybe you can record it and show us using Jing http://www.jingproject.com/