Mark1234 - If we solve your problem for a balanced level turn, with altitude and velocity stabilised throughout. The max angle of bank will be limited by the power available to maintain speed. To a first order that will be independent of configuration (actually depends on Cl/Cd at Cl-max).
For an example, let's say that this is at a load factor of 2 and hence for a 60 degree angle of bank.
In a stabilised turn at that angle of bank Cl-max will be reached at 1.4*Vs.
Let's assume that flaps increase Cl-max by 20% and so decrease stall speed by 10%.
The radius of turn is dictated by the centripetal component of lift and is proportional to (Velocity^2/tan(bank angle)).
As we have fixed bank angle for the two cases the radius of turn will be proportional to the square of the velocity at which you reach Cl-max.
So lowering flaps and increasing lift means that you reduce the velocity by 10% and hence reduce the radius by 20%.
The assumptions that I've used are far from perfect, but, I hope, explains the basic reasoning for using flaps and buffet speed (buffet is close to AoA for Cl-max) to minimise the turn radius.
Hope this helps.
M1