Pretty much the whole question right here. I’m guessing that when ships are tacking that the flag may fly at different angles from the ship, but when the sails are full, with the wind behind the ship, does the flag fly in the same direction as the ship or does the flag fly pointing back away from the ship. My first guess would be that the same wind which fills the sails also “pushes” the flag, but I’m not sure. Does the ship sail fast enough to make the flag fly in the opposite direction that the ship is going?
Forward, with the wind.
A sailboat can’t go faster than the wind pushing it…
If the ship is on a dead run (traveling in the same direction has the wind), and is powered only by sails, the sail is going to be blown towards the bow.
A boat sailing on a dead run can not sail faster then the wind–the faster the boat goes, the lower the apparent windspeed.
If the boat isn’t sailing on a dead run, then it’s possible for the boat to go faster then the windspeed (relative to land), and things get a lot trickier for that flag…
(Just to be a little more clear–a “dead run” means travelling in the exact same direction of the wind. Any other angle then that and things change.)
I have only been on a sailboat once in my life, for about 2 hours. I seem to remember the wind blowing against my face as I stood looking ahead of the ships movement.
This, of course, makes no sense now that I think about it. Maybe the wind was blowing from behind me, and my memory is being confused by all of the other forward-acceleration experiences I’ve had in my life.
It’s very simple.
Flags hung from sailing ships, like ensigns or signal flags, stream with the wind.
Relative to the ship, they could be “pointing” in almost any direction, depending on the point of sail. They’ll be going one way on a reach, and somewhere else on a tack.
If your sails are flogging and your banners are astern, you screwed up.
This is not only possible, but likely.
You were on a tack, and if the boat’s best point of sail was only a few degrees off the wind it could appear that you were sailing upwind.
Your first guess is correct. With the wind moving in the same direction of the ship, the ship can’t sail faster than the wind pushing it. Therefore, the ship can never sail so fast such that the flag would blow in the opposite direction.
Incidentally, this is why “heads” (latrines) in old sailing ships were at the bow (or head) of the ship, so as to blow odors forward of the ship.
It’ll make sense if you think about it a little more. 
Say the wind is coming from the north (0 degrees). Say your boat is oriented perpendicular to the wind–lets say your bow is pointed dead east (90 degrees). Let’s say your anchored. From your perspective on the boat, all the wind is coming from 0 degrees, obviously. Now, you cut your anchor, and you start moving. Your movement through the air creates “wind”–it’s the same as if you stick your hand out of a moving car, only more subtle. This wind “adds” to the real wind, and makes the “apparent wind” seem to come from some direction between 0 and 90 degrees (the exact angle depending on your speed–the faster you move, the further forward the wind seems to come from).
This effect happens on all points of sail, except straight downwind.
It’s also possible that you were sailing into the wind on a tack, in which case it’s even easier to understand why the wind seemed to be coming from the front.
Thanks all for the quick responses. Before I posted this thread I went to google images of sailing ships, but the problem was that most of the images weren’t photos but paintings and half of those (at least) had the flag flying the “wrong” way.
Googling ‘yacht’ seems more productive.
Thanks.
By the way, I was looking at those yachts and found this great pic, but it didn’t have a flag. http://www.constructionlounge.com/images/funny%20pics/redneck%20yacht.JPG 
Sorry to continue a hijack, but holy cow.
Imagined conversation between group of 12 year old boys with scrounged lumber, nails, and a couple of hammers:
“Hey, let’s build a fort!”
“No, no, let’s build a boat!”
“Naw, let’s play in the abandoned trailer in Old Man Trumbley’s yard!”
“Can’t we do all three?”
all together: “…YEAAHHH!”