The higher-twist (HT) contribution to the charged-kaon pair production in the high energy proton-antiproton collisions at large transverse momentum p(T) is investigated by using the frozen coupling constant approach for various kaon distribution amplitudes (DAs), which are predicted by light-cone formalism, the light-front quark model, the nonlocal chiral quark model and the light-front holographic AdS/CFT approach. In the numerics, the dependencies of the HT contribution on the transverse momentum pT, the rapidity y, and the variable x(T) are discussed with special emphasis put on DAs. The HT contribution is also compared with the leading-twist ones. It is shown that the HT contributions are dependent on the kaon DAs and also some other phenomenological parameters such as momentum cutoff parameter Delta(p). Inclusive kaon pair production presents a remarkable test case in which HT terms dominate those of LT in certain kinematic regions. The HT direct production process via gluon-gluon fusion contributes significantly to the inclusive cross-section at large p(T).