I have fresh flounder that I have to freeze. What's the best way to package it for freezing?

If I have to freeze fish, I always use this method: place the fish in a plastic freezer bag, fill with enough water to cover the fish, carefully fold the bag while pushing out as much air as you can; seal and freeze flat. The fish never dry out.

The Vacuum sealer is the best option. But there's a cheaper option now.
Ziplock makes a small hand pump for removing air from their (specialized) bags.
The bags have a coin sized 'spot' where you place this little pump to vac out the air.
They sell gallon sized bags. The pump and 3 small bags in the starter kit are only 5 dollars. Most supermarket have them now in the bag/foil/wax paper section.

I have both foodsaver and that..and I use the vac ziplock bags for short term storage of cheeses, you can re-zip them and pump out air for daily use---without wasting 2 inches of foodsaver bags.

The seals can break sometimes..so check from time to time. It's 5 bucks..so don't expect heatseal tech..but it works very, very well for what it is.
I think that would work just fine for fish stored for a few months frozen.

Fished flounder as a kid...my dad would always put like a pound of filets in a plastic bag, squeeze out the air, then immerse the sealed bag in a plastic quart container. Lasted months that way.

And try to cook the fish as soon as possible!!

I would do plastic wrap, then aluminum foil, then freezer bag. I have read that this method is the best for preventing freezer burn. Also, freeze as soon as possible and in small portions, if you'll want to defrost smaller portions.

If you have access to a vacuum sealer its best in my opinion, if not wrapped well in plastic and placed in a freezer bag making sure you press all the air out of the bag before you seal and that way you will avoid the possibility of freezer burn.