Ac light flickers and the the engine runs rough

Sounds like it just needs a service maybe. If no lights are staying on it would seem to be nothing serios but a service may be advisable to check just in case. Rough idling may just be down to needing new spark plugs/cables or a distributor cap.
Best to be on the cautious side I think, it often saves money in the long run

GOOD LUCK TO YOU!

I would first recommend getting the OBD codes read as could be a switch/sensor , but the previous postees all have valid opinions

Have your a/c compressor looked at. It sounds like it may have went bad putting a massive strain on the engine while the a/c clutch is trying to kick on. a bad compressor would make the a/c light flicker or turn on and off. Until you get it serviced I would pull the fuse or turn off the a/c. When it completely locks up you will lose your surpentine belt.

IF THIS HAPPENS ONLY WHEN THE AC IS SWITCHED 'ON', THE AC CLUTCH MAY BE DEFECTIVE