Burgundy is a very difficult colour jacket to wear. If it's a really saturated burgundy, charcoal grey works well. Cream flannels are another option. I would avoid mid-grey (it looks a bit front-desk with a burgundy jacket). Brown could theoretically work, but I suspect it will be hard to avoid looking the colours looking "muddy" against each other. Perhaps tan might be a better choice. If you're going the peacock route, and the burgundy has enough blue in it to veer a shade towards purple, then I can actually imagine mustard cords looking great against it, with a blue OCBD shirt, or normal ecru/cream shirt & a wool or knit tie.