I just noticed today that all the lights on my 99 Z28 are flickering the the Volt gauge is moving up and down. Could it be alternator or battery are going out? What could be the problem??

 

Check your grounds, make sure there tight and clean. There's the one under the hood on the passenger side strut tower, there's also one on each side of the dashboard at the bottom.

 

As suggested, check the grounds.
I suspect the internal regulator of the alternator is on its way out the door.
You might for troubleshooting purposes, remove the red wire from the BATT stud on the alternator and insulate the terminal on the wire, jumper cable a running vehicle to the faulty vehicle, turn on the faulty vehicle engine and check to see if the same symptoms appear.

If the flickering appears, then bad grounds or cabling.
If no flickering, then faulty alternator on faulty vehicle.

 

never unhook the battery when the engine is running. good way to burn out the regulator. i would start by cleaning the connections at the battery, take both cables lose and wire brush the heck outa them and do the same to the battery terminals. then go the the power junction box (small red plastic box on the passenger side fenderwell by the battery) and take the wires lose and wire brush the heck outa them to. i believe the ground for the gauges is on the driver side door jamb under the kick panel. so headlights blinkers dashlights all go out?