As with every style, flat design should be used in websites and products where the look fits the target and objective of the product. Not all websites or apps will benefit from using a flat aesthetic design. A flat design look is, indeed, really flexible and can be used in very different types of markets and targets, but always keep your objective in mind. Use flat only if it makes sense for the project in hand. Each project is different and how you want to convey the message in your website or interact with your users through your user interface varies from project to project.
Flat can be easily used and found in designer portfolios, corporate websites, web apps, mobile apps, restaurants, and a lot of other different examples, but you need to ask yourself this question: is flat a good look for my website? If you're creating a game website, such as a RPG, or promoting a premium and expensive product, such as a watch or a good wine, you're probably better off...