Flat design has taken the web and mobile by storm. Like any trend, both seasoned and aspirational designers are using elements of flat design to different degrees of success. Those that nail it usually have an eye for white space, iconography, and most importantly, typography.
Minimalism is at the heart of flat design. Sans serif typefaces are usually used throughout for consistency and clean lines. Type families that have a full range of weights are preferable for maximum contrast, especially on bright simple backgrounds.
Most flat design makes typography the star. Big bold headings with smaller but highly legible subheadings are key in clean, flat layouts. What makes that look visually appealing is the focus on hierarchy. Directing the user's eye to the most important information first makes the UX more intuitive.
Leading and tracking gives typography room to breathe. Any good flat design is tightly edited for clarity and brevity. Once you have that final text, it should be easy to give your layout a lot of breathing room. Concentrate on the leading and tracking throughout to give the text a consistently easy-to-read flow.