Lets not consider any compressibility effects, nor changes to wing area by the deployment of flaps. Then obviously for 1 G flight, for the same speed, the Cl will be the same for all flap settings.
You can figure out the max Cl for each flap setting if you know the stall speeds for the different configurations.
The maximum Cl for each setting will be the max Cl for zero flap times the ratio (Vstall clean divided V stall with flap extended) squared. Speed in calibrated.
All comes from L=.5* p * S * Cl *Vsquared
Hawk