Is the flare nut that connects the flexible brake hose to the brake line connected to the flexible hose or the rigid brake line??? I looked at a couple of parts diagrams and can't tell.

 

yes, only use flare nut wrenches when dealing with "plumbing"

 

after, re-reading...

 

Looking at your pic, which way does the flare nut get turned to loosen it? towards the ground or towards the sky??

 

Depending on placement of wrench, it could be both. If wrench on left side of picture, toward sky, if wrench is on the right side, toward ground.
Remember lefty loosey righty tighty, counterclockwise (lefty) clockwise (righty)