I would flush clean the pen only when I've run the pen dry. IOW there is no ink left in the pen to worry about putting back into the bottle or not. And even then, I will not clean the pen every time I empty the pen. Heck I have some pens that have not been cleaned for MONTHS, and they work just fine. But, as has been said, some inks do need cleaning more often/frequently than others, because the ink so saturated that it will gradually clog the feed. Also how often you use the pen also affects this, as infrequent usage could result in the ink drying in the feed. So bottom line is, it depends on YOUR specific ink/pen/usage combo.
The only time that I will clean the pen between fills, with ink still in the pen, is when I have a nib clog. Some papers leave a LOT of paper dust on the nib that migrates into the nib/feed, and clogs the pen. Then I need to flush clean that gunk out of the nib/feed.
Normally clip pens are stored nib UP. But there is nothing wrong with storing the pen flat. Some pens, however, need to be stored flat or nib down. This is because the ink gets stuck in the back of the converter when stored nib up, and you have to open the pen to tap the converter to get the ink to fall down to the front of the converter. This is why some converters have a stainless steel ball inside. The ball falls through the ink breaking the surface tension that is holding the ink to the back of the converter.
I will store the pen lying flat then, If i start noticing issues with that, then I will store it upright, I am guessing this is a logical way of thinking.