From your description it sounds as if whatever display the selfview is on begins flickering, regardless if it's HDMI 1 or 2 output. Try swapping the HDMI cable between the SX20 and the camera, if the issue still persists, you'll need to swap the camera with one from another codec if you possible. You'll want to swap the questionable camera to a second SX20 to see if the camera is faulty, and at the sametime, take the second camera and put it on the first SX20 to see if it could also be the codec.
Check to see that the you have the powerline frequency (can be found in the web interface under Configuration > System Configuration > Cameras) to the frequency used in your area (50Hz or 60Hz). I've noticed that the "Audo" setting doesn't always work nicely.