Induced drag is the drag induced by the lift and, from memory,
Cdi = kClsquared / Pi AR where :
Cdi = Induced drag coefficient
k is a constant dependant upon the span-wise lift distribution with k=1 for a perfect elliptical distribution,
Cl is lift coefficient
Pi is Pi
and AR is Aspect Ratio
So flap deployment will change the span-wise lift distribution - assuming the flaps are not full span (the form drag will certainly increase) - thus changing k and thus changing Cdi
Flap deployment will change the wing area (assuming some type of area-increasing flap such as Fowler or dropped hinge) and thus the Cl and thus Cdi
Methinks induced drag will change with flap deployment!