Dendrite growth is a typical liquid-solid phase change phenomena that extensively exists in engineering. Deep insight into its transition details and mechanisms from multiscale views will help understand and optimize its behaviour. In the present study, a dendrite growth model coupled with thermal convection governed by Boltzmann model equations is proposed. The Shakhov-Boltzmann equation is utilized to evaluate the thermal compressible fluid flow with a flexible Prandtl number; the BGK-Boltzmann equation with an anisotropic factor is implemented to simulate dendrite growth which can be recovered to the well-known phase-field equation. The two equations are discretized and coupled by discrete kinetic scheme (DKS) method. On account of the asymptotic preserving property of DKS method, the present model is capable of modelling phase transition at a large range of spacial and temporal scales and its interaction with fluid in distinct flow regimes. The DKS model is verified and validated by several benchmarks. For flow dynamics with heat transfer at different Knudsen numbers, lid-driven flow case was conducted to compare with the results by Direct Monte Carlo simulations; the cases in continuum regime of compressible and nearly incompressible were tested as well. Additionally, flow passing around a solid barrier is simulated to verify the solid-liquid interaction based on the diffuse interface description. The anisotropic phase transitions under pure thermal diffusion and convection were simulated consequently. These evolution results demonstrate that the model is of good performance in accuracy and stability, and is competent in addressing multiscale calculations. Furthermore, a two-dimensional single equiaxed dendrite growth simulation is conducted with thermal flow from rarefied regime to continuum fluid. It is found that under different scales, the dendritic interface exhibits different dynamical and morphological behaviour dominated by various flow and heat transfer patterns. The rarefied effect will significantly change the heat transfer process which shows great departure from Fourier's law, and dominantly contributes for the final phase interface structure. In conclusion, the DKS model would produce a novel viewpoint and a predictive method to investigate phase change phenomenon in different flow regimes.