Jay, I recommend that you have your house wiring inspected by a licensed electrician. Lights dimming, and lights blinking are two different things. 1) When I go to my work shop and fire up my radial arm saw the lights in the shop momentarily dim until the motor comes up to speed, and then they go back to full brightness. This happens because the slug of current that a motor draws trying to start can be 5 or 6 times the normal running current, and cause voltage drop in the wires on that circuit. Local lights will dim due to the reduced voltage. The same thing used to happen with the refrigerator in the kitchen until I rewired the kitchen. 2) Lights actually blinking off to totally dark, or a dimming condition which has become dramatically worse lately, or a dimming condition accompanied by over brightening can be associated with loose or deteriorated connection in the main panel. Loose and deteriorated connection in the main panel have caused home fires and should be checked out by a responsible electrician. Please don't ignore the situation, your safety and that of your family may depend on it.
If the electrician reports that your home is okay, then contact your local electric utility, they could have a problem with their connections. BobB