We investigate the information which could be obtained from Drell-Yan processes with sufficiently intense beams of charged kaons on isoscalar targets. It is found that combinations of $K^+$ and $K^-$ Drell-Yan measurements on isoscalar nuclear targets would allow one to extract the kaon sea quark distributions. These cross sections are also sensitive to the strange valence quark distribution in the kaon, although one would need a significant increase over the presently available kaon fluxes in order to extract this quantity with sufficient accuracy.