Using the extended Huygens-Fresnel principle in this paper, a semi analytical expression for describing the on-axis scintillation index of a partially coherent flat-topped array laser beam through slant path of non-Kolmogorov atmospheric turbulence is derived; consequently, with the help of the log-normal intensity probability density function, the bit error rate (BER) is evaluated. The main aims of this paper are exploring the effects of source factors (such as wavelength, order of flatness, and beam width) and the non-Kolmogorov turbulent atmosphere parameters (such as Kolmogorov inner scale, general spectral power-law exponent, the turbulence structure constant) on propagation behaviour of scintillation index, and, hence, on BER. Results indicate that, when the average SNR increases, BER is more affected while the power-law exponent increases. Consequently, it can be deduced that the mean bit error rate increases while the power-law exponent decreases. In addition, the scintillation index and BER as communication link parameters represent the fact that increasing the atmospheric refractive-index structure parameter on the ground and decreasing the inner scale of turbulence eddies, which expresses the conditions of strong turbulence, causes an increase in theses link parameters.