I contend that the major reason for tip stalling with flap down is that the different Cl over the inboard section caused by change in camber, a of a and possibly wing area allows the tip to stall, first.
But the effect of flap is to raise the local Clmax - Cl at all spanwise sections must be considered in relation to the local Clmax. None of the foregoing explains the reason that you seek.
I refer you to
NACA Rept 829 Inboard flaps do not always result in an outboard stall. If student pilots want a simple, general theory that fits in with their trainer's characteristics then try this: "Flap deflection generally tends to aggravate the stall by increasing the upwash over the outer unflapped parts of the wing and by cleaning up the area of separation at the root."
Or put another way the transition point moves further back on the inboard section
You've lost me there. Transition point is defined with respect to the boundary layer - transition from laminar to turbulent. Transition point is a significant factor for aerofoils which have a leading edge stall but otherwise it doesn't really fit into this present debate. Stall of a flapped section is generally over the rear part of the wing.