There is no built-in flash, but you can attach an external flash to the bracket provided. The settings also offer different modes for working with an external flash. This is a good solution, because a built-in flash would have been of poor quality anyway. With an external flash, the quality is optimal and you don't use the ZV-1's battery. Alternatively, you can buy an external flash that doubles up as a projector, which will be handy for videos. Having said that, I chose the ZV-1 for its ability to work in low light, so I almost never needed a flash.
No, the ZV-1 camera comes without an integrated flash, but has a multi-interface shoe to which a flash unit can be attached and which can be triggered via the camera.