The battery light is flickering on and off on the dash. I put a new battery in and had my alternator checked out(its prefect) When driving at night my headlights dim and brighten.What could this be?

Loose wires to the headlights or fuse panel.

It could be a couple things. Take it to a shop or a place like auto zone and have them test the alternator and the battery, its free :) If they both are testing as good, the next thing would be to check the battery terminals and connections. It simply is not getting the enough charge back to the battery for one reason or another.

could be but check the drive belt first for condition and tension

Have an auto electrician check out the wiring of the car. there could be a short somewhere in the wiring

check the alternator output

I would check your fuse board for a loose fuse or wire to it from the battery as sometimes vibration loosens terminals eric

This sound like a loose conection at the batter or alternator. Check to make sure all the conections are tight and snapped in place securely.

check all battey connections and system grounds. Check that the battery has 12v and holds properly when load tested. To check charging system, don't disconnect any battery leads...put a volt meter across the battery. when running, you should have at least 12.9v and volts should not drop. (usual reading is generally at or near 13) at idle with all accessories on voltage should be close to that as well. voltage should not exceed 14.Also make sure that drive belt is not slipping.

check the connections to your altenator, and your battery ground cable

Have the battery checked.  You may have heard a fast clicking sound when the lights were flickering, if so it's coming from the starter solenoid.  If the battery is bad, have the voltage regulator and alternator checked also.  A bad voltage regulator or alternator will kill the new battery.    

Try starting with jumper cables, if that works, you can pull the battery out, take it to a auto parts store that will test it for free (most parts stores will do this).  If it's bad, you can put a new battery in and then drive straight to somewhere to have the charging system tested.