Flat design become popular in responsive design era because its based on simple elements without any illusion of three dimensional space.
Elements that provide the three dimensional illusion, such as borders, shadows and textures are omitted in flat designs.
Therefore, flat designs are focused on a minimalist use of simple elements and flat colors.
Such elements create a clean user interfaces that can be reproduced perfectly on all screen sizes.
If website is based on the flat Joomla template, it will give the same feeling on all devices used to access it.