Spatial diversity as well as multipath diversity can be exploited by Space-Time (ST) coding techniques in the presence of frequency-selective channels. A new class of linear ST codes, known as Khatri-Rao ST codes, have recently been proposed for the flat-fading channel scenario. These codes provide built-in blind channel identifiability and rate diversity flexibility. We study the extension of these codes to the frequency-selective channel case. These codes can handle any transmit/receive antenna configuration and signal constellation. They are designed to achieve the maximum possible spatial and multipath diversity in scattering rich frequency-selective channels, equal to the product of the number of antennas and the number of FIR channel taps. The proposed codes are shown to have desirable properties like guaranteed unique linear decodability, built-in blind channel identifiability and efficient near maximum likelihood decoding.