Runs rough at idle, check engine light is now flashing

The check engine light flashing is trying to tell you that you're in imminent danger of catalytic converter damage. This is probably caused by a misfire which is the cause of the bad running. I'd check the ignition system, the first thing I think of is defective sparkplug wires arcing to the block in the moist weather. Check that first. If you want to find a Jag specialist, here's a directory link for you: https://repairpal.com/jaguar-repair-in-okatie-south-carolina