The Standard Model (SM) explains CP violation in terms of the CKM matrix. The BABAR experiment was designed mainly to test the CKM model in B decays. B decays that proceed through b {yields} s loop diagrams, of which B {yields} KKK decays are an example, are sensitive to new physics effects that could lead to deviations from the CKM predictions for CP violation. We present studies of CP violation in the decays B{sup +} {yields} K{sup +}K{sup -}K{sup +}, B{sup +} {yields} K{sub S}{sup 0}K{sub S}{sup 0}K{sup +}, and B{sup 0} {yields} K{sup +}K{sup -}K{sub S}{sup 0}, using a Dalitz plot amplitude analysis. These studies are based on approximately 470 million B{bar B} decays collected by BABAR at the PEP-II collider at SLAC. We perform measurements of time-dependent CP violation in B{sup 0} {yields} K{sup +}K{sup -}K{sub S}{sup 0}, including B{sup 0} {yields} {phi}K{sub S}{sup 0}. We measure a CP-violating phase {beta}{sub eff} ({phi}K{sub S}{sup 0}) = 0.36 {+-} 0.11 {+-} 0.04 rad., in agreement with the SM. This is the world's most precise measurement of this quantity. We also measure direct CP asymmetries in all three decay modes, including the direct CP asymmetry A{sub CP} ({phi}K{sup +}) = …