You might not need flash. Digital cameras are quite good at shooting in low-level ambient light, either daylight from a window or artificial light. You can change the ISO setting to increase the sensitivity of the camera to light. All Canon digital cameras offer ISO 1600; the top of the range EOS-1D X offers up to 204800!
The downside of high ISO speeds can be increased ‘noise’. Canon cameras use advanced noise reduction technology to minimize the effect. Take a few test shots at high ISO speeds to see if the results are acceptable.
In ambient light, the camera might set quite a slow shutter speed. Keep an eye on this. If the shutter speed drops below about 1/60 second you might need to use a tripod or support the camera on a table or chair back. You will also need to ask your subject to stay still for a moment as you take the picture.