A simple question really, i'd also like an explanation of whether or not stars are flat.
In answer to your question, no, stars are not flat.
Here's a quick explaination why.
Sustainable nuclear fusion on that scale only exists as a sphere. The power generated during the fusion process is constantly forcing the star apart, meanwhile the immense mass of the star's gas is constatly crushing back toward's its centre. This is why stars expand as they grow older, as the star fuses matter, there is a certain amount of mass lost in this process which is converted into energy. As the star loses mass, the forces generated by the fusion process allow the star to expand further. For a perspective of how much mass is lost, the fusion reaction within your average thermonuclear warhead is only a few grammes, put that on the scale of a star, and we're talking a lot of mass conversion per second.
In simple terms, the star's own immense gravity forces the fusion process into stability within the star's core, which is impossible to achieve with a flat disc.