Superpartners of goldstino -- scalar and pseudoscalar sgoldstinos -- interact weakly with ordinary particles. One or both of them may be light. We consider a class of supersymmetric extensions of the Standard Model in which interactions of sgoldstinos with quarks and gluons conserve parity but do not conserve quark flavor. If the pseudoscalar sgoldstino $P$ is light, m_P(m_K-m_��), an interesting place for experimental searches is the poorly explored area of three-body decays of kaons, K^0_{S,L}\to��^+��^- P, K^0_{S,L}\to��^0��^0 P and K^+\to��^+��^0 P, with $P$ subsequently decaying into ����, possibly e^+e^-, or flying away from the detector. We evaluate the constraints on the flavor-violating coupling of sgoldstino to quarks which are imposed by K^0_L-K^0_S mass difference and CP-violation in neutral kaon system, and find that these constraints allow for fairly large Br(K\to����P). We find that the most interesting ranges of branching ratios start at Br(K^0_L\to����P)\sim 10^{-3}, Br(K^+\to��^+��^0 P)\sim 10^{-4}, Br(K_S^0\to����P)\sim 10^{-3}. These searches for light pseudoscalar sgoldstino would be sensitive to the supersymmetry breaking scale \sqrt{F} in the 100 TeV range and above. We also briefly discuss the cases of light scalar sgoldstino and relatively heavy sgoldstinos.

14 pages, 3 figures. References added. Journal version