For the best chance of success you want to shoot in good, strong light (sunlight!) with the sun behind you. Use centre point focus only, AI Servo and you'll need to be very accurate with your aim to keep the focus point on a contrasty part of the dog. Aim for the eyes/teeth. An all black dog is a nightmare - the camera needs to see contrast in order to focus.
Use the long end of the lens - 250mm - this will mean you can shoot the dog at longer range, which will reduce the relative speed at which the dog closes distance between you.
In my experience 1/400 is too slow. You may have problems with AF but you probably aslo have problems with blur. I'd be looking to shoot a running dog at 1/800 or faster. f/5.6 should be plenty to keep the dog sharp, if the focus is good enough. Assuming you have bright sunshine then you could shoot at 1/800, f/5.6, 100 ISO. If you bumped the ISO to 200 you could stop down a little, perhaps to f/7.1 for a little more DOF and to give the AF a helping hand. It should also improve lens sharpness a little. You will also be able to nudge the shutter speed up to 1/1000, which should be good enough. If the light isn't full sunshine then you'd be better off bumping the ISO again, to 400, rather than compromising your shutter speed.
Here's an example at 400mm, 1/1000, f/7.1, 800 ISO....
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at 400mm, 1/1250, f/8, 800 ISO....
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