Flash has quite a few solid advantages
Animated Graphics
This has long been the strong suit for Flash. Stunning effects on a Flash Template are easily handled and it can give a website the looks to differentiate itself from the others.
Vector Graphics
These are special types of pictures which have the good reputation for looking really clear in the web browser. As opposed to bitmap images, vector graphics are rather pieces of code than colored dots - that's the reason that resizing doesn't distort or pixelate vector images. That's because of vector graphics that Flash templates have all the highly detailed animations and sleek lines and borders.
Video
Embedable movies on Youtube and webpages is just another thing Flash is popular for. Now again, the Flash makes it no big difference what OS you have - videos or animation will be rendered beautifully, one and only thing you need is deploy the Flash player plugin.
Compatibility across Platforms
Out of all the popular browsers Flash templates are supported on the vast majority of them. Roughly 95% of all internet browsers have the ability to render Flash really well. The basic premise and an important feature about Flash is the fact that a simple web browser plugin makes Flash viewable in the same manner across the majority of the modern day web browsers, no need to point out that the major ones - IE, Firefox, Google Chrome and Safari render Flash easily.