The best place to gig for flounder is off of the East Beach flats. Thats all of the way to the end of the island toward Bolivar. The water is very shallow out there for quite a ways.
BBB was right it is better during the runs, but it was always a way to spend a Saturday night when we were kids. Me and my buddy would go out before midnight and get one limit, then come back in and go again after midnight and get another one. Then we go down to the poor side of town and sell 'em!
There are other places if you have a boat, but this is the easiest for a newbie. Please, Please, Please watch for stingrays! They will ruin your whole night. Or better yet invest in a pair of guards. I used up all of my luck back then I guess cause I never got it. I was out one night, noticed something off-color and poked at it only to have the entire ground in front of me take off and see a large tail go right past my shin.
Now every time I play the lottery I never get anything.