'Cycle chic' - of the great and well-known Copenhagen bike and street fashion blog - has the luxury of being a descriptive term, celebrating what already exists in spades there. Here it would function more as a directive, or a desperate plea, and I wouldn't presume to ask Washingtonians to cycle chic(-ly). People here often dress well, but fashion is not really a DC strength. I do think we're capable of a kind of cosmopolitan civility. I don't think our hardworking and sometimes wonkish masses would rally around 'chic'.
So, how to vastly increase the number of people on bikes on a daily basis, as part of the city fabric? It has to appeal to the masses, as basic urban transport.
The city is trying to do its part, with more and better bike lanes and infrastructure. But in many ways it starts with a certain riding mentality and the bicycles themselves - slower, with a more upright sitting position; chainguard, fenders, rear skirt all mean you show up unsplattered on rainy days; staying out of the thick of traffic means a helmet is not as necessary (more on that to be sure).
So you can hop on and go, without special clothes or an alternative lifestyle. Ride as you are. Ride in heels or a suit. Ride chic(ly) if that's you. Don't wear a helmet, or do. Take your time. Try to generally follow traffic laws, and be civil as a way to defuse the anti-bikers. Think of yourself as part of a graceful, heightened, aesthetic (yes!) urban experience. Turning the North American negative connotations of 'urban' upside down, reclaiming the beauty of civilized city life.
Citizen Cycling. Better biking, better cities.