When should I use the global Reynolds number and when the local Reynolds number?
Definitely use the local Reynolds number on each of the flaps! The flap will only work properly if it is allowed to produce its own, fresh boundary layer. If instead it inherits the slow, thick boundary layer of the wing or flap ahead of it, the flow would soon separate and the flap would loose most of its effectiveness.

Note that a Reynolds number is always a local phenomenon. At 2 m from the leading edge, the Reynolds number is twice as large as at 1 m. Only when you compare total coefficients for the whole airfoil would the Reynolds number at the trailing edge be used.

If the distance between your bodies is more than a few centimeters, the boundary layers will not interact, so again the local length should be used for the Reynolds number reference length.