Speaking from the perspective of the Royal Navy, ships made their own flags, banners, pennants, etc. and dockyards that came under naval discipline would as well. A sailmakers crew could run up a jack in an hour or so, depending on the size. I don't think it would have taken any appreciable amount of time at all. Incidentally, ships of the day generally kept multiple national flags around, as well as signaling flags (though signaling was far more advanced in 1801 than 1701) -- the national flags would be used to conceal a ship's identity or as private signals between ships in the same navy.