My experience? We are usually not encouraged to use flash AT ALL when taking photos in a competition area like the dog's version of a standard obstacle course, obedience competition, and all that.
The places where it's usually allowed is the beauty contest and the best costume/misc competitions. Unfortunately if you are the one with the big camera with your flash switched off, people will still look at you evilly when giving warning out when the guilty ones are the ones with their P&S cameras.
i think that it is not tat nice to use flash as you never know it might excited or irriated the dog. just 1 thing to highlight: use fast shutter speed.. i think min.. 1/125 as they are keep moving and pay attention to focusing.. so.. i think use high ISO setting and fast lens as mentioned by snowspeeder
Beware, using flash on dog might produce red eyes effect on your photo which is very obvious.
If you are covering the show/demo, it is always good to ask the orgainser, try not to shoot flash direct at the dog when they are doing stunt, maybe at angles.
I did once for SKC, good experience. Also remember that if it is indoor, you need fast lens and use a higher ISO so as to freeze action else you will get all the motion blur... depend on what you want.
Just to take note, in the competition area, normally they dun allow flash photography unless you are the official photograher.