Running rough and check engine light came on & started flashing

The check engine light is in response to the misfires. You need to have the system scanned to see if it's random misfires or if it's a specific cylinder. From there testing can be done to determine if it is an ignition coil failure or something else. Misfires can damage the converter(s) because they dump unburned fuel into them which then ignites and causes damage. As such the automakers add in multiple items to protect those units. The flashing light is meant to show that you could be damaging them and should not operate the vehicle.

Do you think I can drive it fifteen miles to get it scanned?

Very hard to say as I do not know exactly what the issue is. If the light comes on but does not flash then drive it to the shop as it has a code but is not really causing an issue at the moment.
If it starts flashing as soon as you start it then I would not drive it. Mainly because it is very hard to say if it would damage anything or not because we do not know what is causing the misfire at this point.
You could buy a code scanner yourself and read the codes but all that would actually tell you is something like a P0304 which is a misfire code for cylinder four. That code could mean that the plug is bad, the coil is bad, that the injector is stuck open/closed that a valve has an issue and more. It is the hands on inspection and testing that is needed.
Unfortunately that is not something I can do remotely, yet.