That's a good idea to replicate the first video in the OP, Indian8or, nice simple workaround. It would be less effective for the second video, with a moving sun, because the relative positions of the lens flare artifacts changes as the light source moves across the focal plane. It might be possible to produce a pretty good simulation of this using your technique, however, with each artifact on a separate transparent plane, animated separately (and carefully). In fact, it may be possible to automatically animate the planes, making them children of a second camera in respect to position, with their orientation locked to the "world". This second camera would be a child of the rendering camera, occupying the same physical space, but set to point at the sun light source.
In the past I have used the frame-by-frame technique suggested by lizeal93, and it is indeed mind-numbingly tedious. The rendering software I use now has the ability to produce this effect automatically (Carrara).
I would also love to suggest attempting to construct an actual lens, based on a 35mm camera lens for example, and placing the camera behind it, but I doubt that this would work, because I am not sure what causes the lens flare effect and whether ART is capable of simulating the necessary parameters. For example, if the effect is caused by a combination of chromatic aberration and caustics, as I suspect, then I don't think this method would have much effect at all. Still, it might be an interesting experiment.