Accessing C++ class (implemented as blueprint) variable by another class

static const APlaneClass* planeClassObject;
or
static APlaneClass* planeClassObject;

in the header is just the declaration you are missing

const APlaneClass* APlaneClass::planeClassObject = something;
or
APlaneClass* APlaneClass::planeClassObject = something;

in your PlaneClass.cpp file

but as Phil said the whole thing sounds a little bit wonky.
Would suggest adding a pointer

UPEROPERTY()
APlaneClass* planeClassObject;

into a Manager that could be in a component on the game mode or game state
the UPROPERTY() is important to prevent garbage collection