Why do lights flash when the car is started?

Do you mean flickering bright and dim or turning on and off?

On older vehicles there was an automatic-resetting circuit breaker built into the head light switch. It would often develop pitted contacts and turn on and off as you described. The fix was a new switch. On most newer vehicles, the engineers have seen fit to add a relatively unreliable computer to the system. The daytime head lamps are incorporated into it. If the head lights AND the tail / running lights flash on and off at the same time, I'd suspect the head light switch or the computer because after that they are on two different circuits. If it is just the tail and running lights that are acting up, it could still be the computer but a more likely suspect would be a loose or corroded terminal in an electrical connector.

Sometimes unplugging a connector and reseating it scratches a clean spot on the terminal and that will make it work properly for a little while but that doesn't really identify the exact cause. It's better to wiggle the connectors while watching the operation of the lights to see if you can find which one affects them. Also wiggle the ignition switch, head light switch, and the parking brake pedal. Any of those can affect when the outside lights turn on and off.