I would suggest to check battery cables first. Clean and tight.
If they are good I would suspect the alternator. A shop that can do a charging system test could probably verify (not sure AutoZone types can do more than check charging voltage).
Another option is to wire a bulb across the battery terminals and see if it flickers too, if it does that would eliminate electrical noise from anywhere else on the vehicle and indicate the alternator.
a lot of time a bad ground from one of the lights is not grounding properly, then system backtracks to find a alternate ground causing lights flicker and some times not operating at all
Most individual lights use their own ground. If the flickering is consistent you can remove 1 bulb at a time until the flickering stops. That should tell you about where the problem is.