I'm wondering what the distance really needs to be. Many people could do something similar if it was plausible to use say the ends of a house, or an office building.

Wouldn't the orientation of the cameras need to be precise? I suppose you could correct for that in software...

I did some basic back of the envelope math to determine what distance it should be. According to http://times-news.com/bobdoyle/x546406583/How-far-away-and-h... an observed Cumulus cloud was about .25 miles wide. If you want it to feel like you're looking at an object relatively the size of a computer screen (I just said 1ft across), and your eyes are about 2.5in across. Then the ratio is 2.5in/12in = Distance_between_cameras/.25mi

Which results in about 300ft or a football field. The you make that distance, the less the clouds will feel like tangible objects.