what color blush to wear with burgundy lipstick

My opinion is that a warm-toned blush would match very well. You may light a peachy blush or a warm-toned pink blush to match it. For a more edgy look, you could also use a purple blush.

what eyeshadow goes with burgundy lipstick

Try a monochromatic look and match a burgundy eyeshadow look to your burgundy lipstick ! I also think that a more neutral, subtle eyeshadow look would look gorgeous, as this makes the burgundy lipstick pop.