In trying to draw up the plans for a patio cover that'll be a solid covered deck for a 2nd story room, I'm trying to find out what slope, if any, is normally required. I've heard 1/8" per ft, and 1/4" per ft. Any professionals out there with the answer? Can't see any specifications in LA County literature.

Contact the local building department. As they have the information that you desire.
What type of deck are you thinking about? Fiberglass or asphalt with a wood deck above?
The smoother the surface (within reason) the less the pitch is required to allow the water to run off. But check with the town the house is located in.