When electronic gauges came out in the '70s that was common. Turn on the ignition and all the gauges would sweep, and all the lights would blink. Some big trucks still do that, but that is not the case with your vehicle. There is a self test feature for Chrysler vehicles, but I don't know what year it started.
It is activated by holding down the odometer knob and turning on the ignition. After going through the sequences, it will display fault codes, if any on the odometer. There could be a fault with the odometer knob allowing this to happen. I would just call a local dealer and ask if this a common occurrence. But, watch out if the dealer says you will have to bring it in for service. You may well have to, but at this point you are just looking for the cause.