Can black ever be uncool? I doubt it. Even a black tank top has attitude. The number one rule, of course, is to take time with clothes and what you wear, but to make the result look effortless. good Jeans, T-Shirts, cashmere sweaters and Bass Weejuns or Desert Boots, are as cool as need be. Timberlands or non-descript brown boat shoes, (the kind I wear, day in, day out), don't make it.(As Frank Zappa would say).
No Cool's wardrobe is complete without a leather jacket, black of course. Make sure it is not one that looks like it has been worn by Peter Sutcliffe. I find the Maquis look works for me, which I sometimes underpin with a black french beret. (you have to be there - some can get away with this, others not.) As for thickness of leather, it should be able to withstand a slug from a Walther PPK at short range, especially if you are meeting Earnest Hemingway in a bar.
And now the rub. It is not possible to look cool in the British climate. Cools can only really look uber cool in California or Southern Europe. In Britain, we have to wear too many clothes for most of the year, so tend to look like Nanook of Nantwich.
1 Black is cool.
2 Unless you are an athlete, wearing anything to do with sports, is about as uncool as you can get. Leave jogging pants to the chavs on the estate.
3 Never wear anything with a designer label on it. You are a dick if you do this. Sorry, no compromise there. Quality and style does not need to spell itself out.
4 For God's sake, change your sock collection once in a while. Why bother with the rest if it looks as if you have borrowed your socks from a bloke who sits by the subway entrance with a dog on a bit of string?