SS304 for Offshore Burner?

No, 304 stainless is a very poor choice for a number of reasons. The primary reason will be sensitization. Virtually all of the 300 series suffer from this phenomena to one degree or another. There is a temperature range between 800 and 1500 degrees F in which carbon forms carbides with the chromium and they precipitate out in the grain boundaries, causing intergranular corrosion and cracking. Even if you were to use one of the "L" series low carbon alloys, the fuel will supply all the carbon you'll ever need to completely trash the burner. You MIGHT have some luck with 347 stainless, but I still think the life will be very limited. Eventually all the aluminum and titanium that was added to preferentially glom onto the carbon instead of allowing it to form chromium carbide will get used up because you will have a constant source of new carbon in the form of the fuel.

One other thing, 300 series stainlesses, and in fact all iron based stainlesses and carbon steels suffer from significant reductions in strength at elevated temps. you might start out at 85KSI yield at room temp, only to be closer to 60ksi at 300 degrees F. You need to make sure that whatever you choose, the strengh level is adequate at the operating temps expected. (make sure to include any thermal transients that the part could experience as well during process trips.)

You should instead be looking at some high temp nickel alloys like those used in hot sections of gas turbines. Nickel prices right now are at historic lows so making it out of a nickel alloy should not be orders of magnitude more than making it out of an austentic stainless like it might have been a few years ago. As long as you stick to the alloys that are "off patent" and made by multiple manufacturers, price should be fairly reasonable. Alloys like 718, Waspalloy, 625, etc. should be fairly widely available and more suitable to this application. They also have good high temp strength as well.

Here is a link from Allegheny Ludlum on their high temp nickel alloys.