Photoshop is more for editing bitmaps (raster images). These are the images that saved as arrays of pixels.

Corel is aimed at vector graphics.Vector images unlike raster are represented by stored elements, like lines or other forms, but not raw pixels.

Flash is a technology mainly for animation. It may use vector or raster graphics for sprites. It is a web tech, where the size matters, because of that vector sprites are often used there.

So these are three different applications. If you need to edit photos or digitally captured images, you should stay with Photoshop. If you are more into drawing by hand, then choose Corel. And if you need aminations, choose flash.