It's hard to tell what the critical current density of LK-99 is, because their sample is porous and probably very impure. They measured the critical current they could pass through a sample, but the conducting cross-section is somewhat unknown. Its high critical temperature suggests that it should probably have a higher current capacity than other superconductors. That said, in the extremes, current density is also limited by tensile strength, because electromagnetic coils repel themselves.