We have cats and they're very tricky to photograph.
Every time I used on-camera flash I'd get the horrible burned out yellow-eye (feline equivalent of human red-eye), so unless you can get the flash off-camera I'd suggest not using it. (Unless it's shots with their eyes shut!)
Last night I grabbed this shot in ambient light in the living room while watching Scream 2.
ISO3200, f/2.8, 70mm, 1/80s, no flash.
Here's one from a while ago with flash.
50mm, f/3.2, 1/250s, ISO100, off-camera flash to camera right.
Another one in which I used off-camera flash camera left trying to give Tigger a moody look.
50mm, f/3.2, 1/250s, ISO100, off camera flash.
If all else fails, try outdoors in daylight, and a long zoom can help avoid distracting them - mine have a tendency to run straight at the camera if they see me with it.
200mm, f/3.5, 1/30s, ISO400.
Good luck!