Lens flare

copy the path and create a new layer with the lensflare design or the lensflare from the effects into a precompose, and then go the position property in that layer and click paste from edit menu or ctrl/command + v. The path autmatically gets copied as an animated position with the lens flare moving that exact path. Later you can increase or decrease the speed of the animation by changing the overall distance between the keyframes in that layer.

I think you're saying you want a path to grow (using Trim paths) and have the leading edge have a lens flare on it?

If so, copy the path to your clipboard, then paste it into the position property of the lens flare effect.  This will get the lens flare moving around the shape's path.  After that, it should be a simple case of lining up its position keyframes to the trim path keyframes.