Over the past decade, polar codes have received significant traction and have been selected as the coding method for the control channel in fifth-generation (5G) wireless communication systems. However, conventional polar codes are reliant solely on binary (2x2) kernels, which restricts their block length to being only powers of 2. In response, multi-kernel (MK) polar codes have been proposed as a viable solution to attain greater code length flexibility. This paper proposes an unrolled architecture for encoding both systematic and non-systematic MK polar codes, capable of high-throughput encoding of codes constructed with binary, ternary (3x3), or binary-ternary mixed kernels. The proposed scheme exhibits an unprecedented level of flexibility by supporting 83 different codes and offering various architectures that provide trade-offs between throughput and resource consumption. The FPGA implementation results demonstrate that a partially-pipelined polar encoder of size N=4096 operating at a frequency of 270 MHz gives a throughput of 1080 Gbps. Additionally, a new compiler implemented in Python is given to automatically generate HDL modules for the desired encoders. By inserting the desired parameters, a designer can simply obtain all the necessary VHDL files for FPGA implementation.