Ok then, some of the above is confusing but here's what I make of it:
Inboard flaps when deployed increase lift (at a given airspeed, Dick), the aircraft balloons until the increased drag reduces the airspeed and hence the lift. Flaps lower the AOA (even during the balloon, I know this first hand from the bit of flight training I've done) To maintain the same lift you need to apply more power but achieve lower airspeed. Thus you can get the same rate of decent at a lower airspeed (but not less power) or a steeper glide angle with no power.
A lower AOA makes it less likely the tips will stall.
My question now is, at the point of stall, does the inner part of the wing with flaps deployed stall first because the higher cambered airfoil has a lower stall angle? (assuming an eliptical wing with uniform section and no washout which in theory would stall at the same time along its length without flaps)