What is "picture flying" and does the FAA define it?
I can't prove a negative, but as CrossRoads pointed out, the phrase "picture flying" isn't used on faa.gov. At least, neither Google nor faa.gov's own search engine turn up any hits.

I searched a bit further and I did find one specific match in a Bendix advert in the Feb 2, 1953 edition of Life:


  Picture flying is the name pilots give to flying with OMNI-MAG. Merely by watching the pointer the pilot always knows where he is,
  where he is going, and how to get there


There's no real technical detail in the advert (it's actually an advert for Bendix television sets!) apart from mentioning that the OMNI-MAG uses VHF radio, but based on the picture it looks like a VOR receiver.

So, given that the FAA seems not to use the phrase at all and the only exact hit I could find was from 1953, I suspect that "picture flying" is an obsolete phrase for following a visual course indication. Before VORs, pilots used audio signals from a four-course radio range and the advert even mentions that they won't have to listen constantly any more.

That makes me think that the phrase arose around the time that radio navigation moved from audio to visual signals, to indicate that the pilot could now look at a visual indicator rather than just listen. That transition happened in the 1950s, so it would fit with the advert's publication.