We have generalized and implemented the hybrid asynchronous algorithm, originally proposed for parallel simulations of the spin-flip Ising model, in order to carry out parallel kinetic Monte Carlo (KMC) simulations. The parallel performance has been tested using a simple model of thin-film growth in both 1D and 2D. We also briefly describe how the data collection must be modified as compared to the case of the spin-flip Ising model in order to carry out rigorous data collection. Due to the presence of a wide range of rates in the simulations, this algorithm turns out to be very inefficient. The poor parallel performance results from three factors: (1) the high probability of selecting a Metropolis Monte Carlo (MMC) move, (2) the low acceptance probability of boundary moves and (3) the high cost of communications which is required before every MMC move. We also find that the parallel efficiency in two dimensions is lower than in one-dimension due to the higher probability of selecting an MMC attempt, suggesting that this algorithm may not be suitable for KMC simulations of two-dimensional thin-film growth.