Well, in my initial glances through the shop manual, the first thing you should do is actually check the tire pressure. Run flats generally don't look "flat" even when they are. The system will monitor the pressure and flash the "LO TIRE" indicator two seconds on and two seconds off if the pressure falls below 20 PSI. Should the pressure fall to 14 PSI or below (considered "critical"), then the flash and chime will be repeated every second. In the event a diagnostic trouble code (DTC) is set, the "LO TIRE" indicator lamp will stay lit until the ignition is turned off. The low tire condition itself does not set a DTC, so to me that means that something else was triggered and the code entered. Thus the flashing indicator light.
Now, as painful as it seems, it is hard to pinpoint in this manual the method for clearing this code. It appears it must be done with a DRBIII scan tool. Addtionally, the tool will point out which wheel had the fault. FASTRNU is correct in that the wheel is then cleared with a magnet (special tool 8821) placed at the valve stem.
Dealer item? Probably. Is your friendly neighborhood Dodge dealer set up for this? Well, I don't know of any Dodge product that has runflats besides the new Viper. Were all dealers given these new tools for a car many have never even seen yet? Don't know. Want to go place a refrigerator magnet next to each valve stem and see what happens?
Let us know what you end up doing, and do check your tire pressure just to be safe...
Chris